# Types of Matrices

## Understanding Different Types of Matrices

Learn about the various types of matrices, including Square, Diagonal, Identity, Zero, Transpose, Symmetric, and Skew-symmetric matrices.

This page includes Quizzes related to Types of Matrices. Here are some basic MCQs with explanations and the best understanding material.

Row matrix
A matrix having just one row is called row matrix.

جس میٹرکس جس میں صرف ایک Row ہو اسے Row Matrix کہا جاتا ہے۔

A=\left[\begin{array}{lll}1 & 3 & 5\end{array}\right]
B=[5]
Column matrix
A matrix having just one column is called column matrix.

جس میٹرکس جس میں صرف ایک Column ہو اسےColumn Matrix کہا جاتا ہے۔

A=\left[\begin{array}{l}1 \\ 3 \\ 5\end{array}\right]
B=[5]
Square matrix
A matrix in which number of rows and columns are equal is called square matrix.

ایک میٹرکس جس میں Rows اور Columns کی تعداد برابر ہو اسے Square Matrix کہا جاتا ہے۔

A=\left[\begin{array}{ll} 1 & 2 \\ 3 & 5 \end{array}\right]
B=[5]
C=\left[\begin{array}{ccc} 1 & 3 & 2 \\ -2 & 0 & 4 \\ -1 & 3 & 6 \end{array}\right]
Rectangular matrix
A matrix in which number of rows and columns are not equal is called rectangular matrix.

ایک میٹرکس جس میں Rows اور Columns کی تعداد برابرنہ ہو اسے Rectangular Matrix کہا جاتا ہے۔

A=\left[\begin{array}{l} 1 \\ 3 \\ 5 \end{array}\right]
D=\left[\begin{array}{lll} 3 & 5 & 2 \\ 0 & 9 & 8 \end{array}\right]
Zero matrix or Null matrix
A matrix in which all the elements are zero is called Zero or Null matrix. A null matrix is generally denoted by O.

ایک میٹرکس جس میں تمام Elements ہمارے ساتھ Zero ہو اسے Zero یا Null کہتے ہیں۔ ایک Null Matrix کو عام طور پر O سے ظاہر کیا جاتا ہے۔

O=\left[\begin{array}{l} 0 \\ 0 \end{array}\right]
O=\left[\begin{array}{ll} 0 & 0 \\ 0 & 0 \end{array}\right]
O=\left[\begin{array}{lll} 0 & 0 & 0 \end{array}\right]
Diagonal matrix
A square matrix in which all elements are zero except diagonal elements is known as diagonal matrix.

Square Matrix جس میں Diagonal کے علاوہ تمام Elements ہمارے ساتھ Zero ہو اسے Diagonal Matrix کہتے ہیں۔

A=\left[\begin{array}{ll} 1 & 0 \\ 0 & 3 \end{array}\right]
B=\left[\begin{array}{cc} -2 & 0 \\ 0 & -2 \end{array}\right]
I=\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right]
Scalar matrix
A matrix in which diagonal elements are same is called scalar matrix.

Square Matrix جس میں Diagonal کے Elements ہمارے ساتھ ایک جیسے ہو اسے Scalar Matrix کہتے ہیں۔

I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]
A=\left[\begin{array}{lll}7 & 0 & 0 \\ 0 & 7 & 0 \\ 0 & 0 & 7\end{array}\right]
C=\left[\begin{array}{cc}\frac{1}{2} & 0 \\ 0 & \frac{1}{2}\end{array}\right]
Note:
Every scalar matrix is a diagonal matrix but every diagonal matrix is not necessarily a scalar matrix.
Identity or Unit matrix
A matrix in which the diagonal elements are equal to “1” is called identity matrix. It is generally denoted by “I”.

Square Matrix جس میں Diagonal کے Elements ہمارے ساتھ صرج “1” ہو اسے Scalar Matrix کہتے ہیں۔

I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]
I=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]
Transpose of a matrix
A matrix obtained by interchanging all rows and columns with each other is called transpose of a matrix. The transpose of a matrix B is written as B^t .

تمام Rows اور Columns کو ایک دوسرے کے ساتھ تبدیل کرکے حاصل کردہ میٹرکس کو Transpose of a Matrix کہا جاتا ہے۔ میٹرکس B کا ٹرانسپوز B^t لکھا جاتا ہے۔

A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]
A^{t}=\left[\begin{array}{ll}a & c \\ b & d\end{array}\right]
Symmetric matrix
In a square matrix, when A^t=A , then A is said to be symmetric matrix.

جب کسی Matrix کا Transposeلینے کے بعد دوبارہ وہی Matrixآجا ئے تو اسے Symmetric Matrix کہتے ہیں۔

A=\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 4 & 5 \\ 3 & 5 & 6\end{array}\right]
A^{t}=\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 4 & 5 \\ 3 & 5 & 6\end{array}\right]
A^{t}=A
Skew-Symmetric matrix
In a square matrix, when A^t=-A , then A is said to be skew-symmetric matrix.

جب کسی Matrix کا Transposeلینے کے بعد اور لینے Minus کے بعد دوبارہ وہی Matrixآجا ئے تو اسے Symmetric Matrix کہتے ہیں۔

A=\left[\begin{array}{cc}0 & 4 \\ -4 & 0\end{array}\right]
A^{t}=\left[\begin{array}{cc}0 & -4 \\ 4 & 0\end{array}\right]
A^{t}=-\left[\begin{array}{cc}0 & 4 \\ -4 & 0\end{array}\right]
A^t=-A
1. \left[\begin{array}{lll}1 & 3 & 5\end{array}\right] is ______ matrix.
O Row
O Column
O Square
O None

Explanation:
Because the matrix consists of only one row.

2. \left[\begin{array}{lll}1 \\ 3 \\ 5\end{array}\right] is ______ matrix.
O Row
O Column
O Square
O None

Explanation:
Because the matrix consists of only one column.

3. A matrix in which number of Rows equal to number of Columns is called ______ matrix.
O Row
O Column
O Square
O None

Explanation:
Definition of square matrix.

4. \left[\begin{array}{lll}1 & 3 & 5 \\ a & b & c \\ 3 & 5 & 7 \end{array}\right] is ______ matrix.
O Row
O Column
O Square
O None

Explanation:
As number of rows and columns are same. Thus, it is square matrix.

5. \left[\frac{1}{2}\right] is a ______ matrix.
O Row
O Column
O Square
O All of these

Explanation:
Here the matrix consists of one row and also one column and also same number of row and column which is square matrix. So, all of these is correct option.
\frac{1}{2}

6. [3] is ______ matrix.
O Row
O Column
O Square
O All of them

Explanation:
Here the matrix consists of one row and also one column and also same number of row and column which is square matrix. So, all of them is correct option.

7. A matrix in which number of row and number of columns are not equal is called _______ matrix.
O Square
O Rectangular
O Null
O None of these

Explanation:
Definition of Rectangular matrix.

8. \left[\begin{array}{lll}1 & 3 & 5 \\ a & b & c \end{array}\right] is ______ matrix.
O Row
O Column
O Square
O Rectangular

Explanation:
As number of rows and columns are not equal, so it is Rectangular matrix.

9. \left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right] is ______ matrix.
O Row
O Zero
O Null
O Both b and c

Explanation:
As Zero or null matrix is same. So Both b and c is the correct option.

10. \left[\begin{array}{lll}0 \\ 0 \\ 0\end{array}\right] is ______ matrix.
O Row
O Zero
O Square
O None

Explanation:
As all the elements are zero in the matrix. That is why, its zero matrix.

11. The zero matrix for \left[\begin{array}{ll}1 & 2 \\ 2 & 4\end{array}\right] is ______.
O \left[\begin{array}{l}0 \end{array}\right]
O \left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]
O 0
O None of these

Answer: \left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]
Explanation:
The order zero matrix must be same according to the given matrix which is 2-by-2 .

12. The product of any matrix and zero matrix is a ______
O Identity
O Scalar
O Row
O Zero

Explanation:
When Zero (0) is multiplied to any number or matrix, the answer must be zero.

13. \left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 9 \end{array}\right] is ______ matrix.
O Diagonal
O scalar
O Null
O None of these

Explanation:
A square matrix on which all elements are zero except diagonal elements is known as diagonal matrix.

14. Scalar matrix is a special case of ______ matrix.
O Identity
O Diagonal
O Both a & b
O None of these

Explanation:
If the diagonal elements in diagonal matrix are same, then it is called scalar matrix.

15. \left[\begin{array}{ll}2 & 0 \\ 0 & 3\end{array}\right] is ______ matrix.
O Diagonal
O scalar
O Null
O None of these

Explanation:
Here all the elements are zero except the diagonal elements.

16. The matrix \left[\begin{array}{cc}-1 & 0 \\ 0 & -1\end{array}\right] is ______ matrix.
O Row
O Scalar
O Null
O None of these

Explanation:
As the diagonal elements are same, so it is called scalar matrix.

17. Identity matrix is represented by ______.
O A
O I
O B
O None

18. Identity matrix is also called ______ matrix.
O Transpose
O Unit
O Symmetric
O None of these

19. \left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] is ______ matrix.
O Rectangle
O Row
O Identity
O None

Explanation:
When the diagonal elements are “1” then matrix is called Identity matrix.

20. I_3 means ______
O \left[\begin{array}{l}1 \end{array}\right]
O \left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]
O \left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]
O All of them

Answer: \left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]
Explanation:
I_3 means, Identity matrix having 3 rows and 3 columns.

21. I_3 is the identity matrix of order ______
O 3
O 3 -by-3
O 3 \times 3
O All of them

Explanation:
I_3 means, Identity matrix of 3 rows and columns. Here all the options show the same 3 rows and columns.

22. A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] is ______ matrix.
O Diagonal
O Scalar
O Identity
O All of these

Explanation:
It is the diagonal matrix having same diagonal elements whcih is scalar matrix and also the diagonal element is 1 which is Identity matrix.
So all are correct options.

23. \left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right] is ______ matrix
O Diagonal
O Scalar
O Identity
O All of these

Explanation:
It is the diagonal matrix having same diagonal elements whcih is scalar matrix and also the diagonal element is 1 which is Identity matrix.
So all are correct options.

24. The Transpose of \left[\begin{array}{ll}1 & -2 \\ 3 & \ 4\end{array}\right] is ______.
O \left[\begin{array}{ll}1 & -2 \\ 3 & \ 4\end{array}\right]
O \left[\begin{array}{ll}1 & 3 \\ -2 & \ 4\end{array}\right]
O \left[\begin{array}{ll}1 & 2 \\ 3 & \ 4\end{array}\right]
O All of these

O \left[\begin{array}{ll}1 & 3 \\ -2 & \ 4\end{array}\right]
Explanation:
When rows and columns are interchanged with each other, then it is called transpose of a matrix.

25. The transpose of \left[\begin{array}{l}1 \\ 2\end{array}\right] is ______.
O \left[\begin{array}{lll}1 & 2 & 3\end{array}\right]
O \left[\begin{array}{ll}1 & 2\end{array}\right]
O \left[\begin{array}{l}2 \\ 1\end{array}\right]
O None

Explanation:
When rows and columns are interchanged with each other, then it is called transpose of a matrix.

26. If A^t=A , then it is a ______ matrix
O Symmetric
O Skew-symmetric
O Diagonal
O None

Explanation:
When the transpose of matrix comes again that matrix is called symmetric matrix.

27. If D^t=-D then it is a ______ matrix.
O Symmetric
O Skew-symmetric
O Diagonal
O None

Explanation:
When the transpose of a matrix is equal to the negative of that matrix.

28. The matrix \left[\begin{array}{ll}1 & 2 \\ 2 & 4\end{array}\right] is ______ matrix.
O Symmetric
O Skew-symmetric
O scalar
O Diagonal

Explanation:
Take the transpose of
\left[\begin{array}{ll}1 & 2 \\ 2 & 4\end{array}\right]^t
\left[\begin{array}{ll}1 & 2 \\ 2 & 4\end{array}\right]
Thus, A^t=A

29. The matrix \left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right] is ______ matrix.
O Symmetric
O Skew-symmetric
O scalar
O Diagonal