Chapter 3 – Matrices
Overview
This page provides comprehensive Class 12 Maths. Chapter 3 – Matrices - Free study material for Class 12 Maths. NCERT Solutions, Notes, and PYQs.
Types of Matrices (Previous Year Questions)
Class 12 Mathematics | CBSE Previous Year Questions
Q1
2023
00:00
Write the order of the matrix $A = \begin{bmatrix}2 & 3 & 1 \\ 5 & 4 & 6\end{bmatrix}$.
The given matrix has 2 rows and 3 columns.
Hence, its order is $2 \times 3$.
Final Answer: Order of matrix = $2 \times 3$
Q2
2021
00:00
State whether the matrix $A = \begin{bmatrix}0 & 0 \\ 0 & 0\end{bmatrix}$ is a zero matrix or not.
All elements of the matrix are zero.
Hence, it is a zero (null) matrix.
Final Answer: $A$ is a zero matrix.
Q3
2020
00:00
Find the value of $k$ if $A = \begin{bmatrix}1 & 2 \\ 3 & k\end{bmatrix}$ is a diagonal matrix.
In a diagonal matrix, all non-diagonal elements are zero.
Here, the element at position (2,1) is 3, which must be zero for diagonal matrix.
But since 3 ≠ 0, the given matrix cannot be diagonal for any value of $k$.
Final Answer: No value of $k$ makes the matrix diagonal.
Q4
2022
00:00
Write the name of the type of matrix $A = [5]$.
The matrix has only one element.
It has one row and one column.
Hence, it is a square matrix of order $1$.
Final Answer: It is a square matrix of order $1$.
Q5
2024
00:00
If $A = \begin{bmatrix}a & 0 \\ 0 & a\end{bmatrix}$, then $A$ is a:
All diagonal elements are equal to $a$ and all non-diagonal elements are zero.
Hence, the matrix is a scalar matrix.
Final Answer: (b) Scalar matrix
Q6
2019
00:00
Write the order of the identity matrix $I_3$.
The identity matrix $I_3$ has 3 rows and 3 columns.
Hence, its order is $3 \times 3$.
Final Answer: Order of $I_3$ is $3 \times 3$.
Q7
2023
00:00
If $A = \begin{bmatrix}2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{bmatrix}$, then $A$ is a:
All non-diagonal elements are zero.
Diagonal elements are not all equal.
Hence, it is a diagonal matrix.
Final Answer: (c) Diagonal matrix
Q8
2020
00:00
Find the value of $x$ if $A = \begin{bmatrix}1 & x \\ 2 & 3\end{bmatrix}$ is a symmetric matrix.
For a symmetric matrix, $A = A^T$.
So element at (1,2) = element at (2,1).
Hence, $x = 2$.
Final Answer: $x = 2$
Q9
2021
00:00
Write the type of the matrix $A = \begin{bmatrix}0 & 0 & 0\end{bmatrix}$.
The matrix has only one row and three columns.
Hence, it is a row matrix.
Final Answer: It is a row matrix.
Q10
2021
00:00
Write the type of the matrix $B = \begin{bmatrix}2 \\ 5 \\ 7\end{bmatrix}$.
The matrix has three rows and one column.
Hence, it is a column matrix.
Final Answer: It is a column matrix.
Q11
2022
00:00
If $A = \begin{bmatrix}a & b \\ c & d\end{bmatrix}$ is an identity matrix, find the values of $a, b, c, d$.
In an identity matrix, diagonal elements are 1 and non-diagonal elements are 0.
So $a = 1, d = 1$ and $b = 0, c = 0$.
Final Answer: $a=1, b=0, c=0, d=1$
Q12
2023
00:00
If $A = \begin{bmatrix}k & 0 \\ 0 & k\end{bmatrix}$ and $A$ is an identity matrix, find $k$.
For identity matrix, diagonal elements must be 1.
So $k = 1$.
Final Answer: $k = 1$
Q13
2019
00:00
How many elements are there in a $3 \times 4$ matrix?
Number of elements = number of rows × number of columns.
So total elements = $3 \times 4 = 12$.
Final Answer: (b) 12
Q14
2024
00:00
If $A = [0]$, then $A$ is a:
The only element is 0.
Hence, it is a zero (null) matrix.
Final Answer: (c) Zero matrix
Q15
2022
00:00
Write the type of the matrix $A = [5]$.
The matrix has only one element.
It has one row and one column.
Hence, it is a square matrix of order $1$.
Final Answer: $A$ is a square matrix of order $1$.
Q16
2024
00:00
If $A = \begin{bmatrix}a & 0 \\ 0 & a\end{bmatrix}$, then $A$ is a:
All non-diagonal elements are zero.
All diagonal elements are equal to $a$.
Hence, the matrix is a scalar matrix.
Final Answer: (b) Scalar matrix
Q17
2020
00:00
Find the value of $k$ if $A = \begin{bmatrix}1 & 2 \\ 3 & k\end{bmatrix}$ is a diagonal matrix.
In a diagonal matrix, all non-diagonal elements must be zero.
Here the element at position (2,1) is 3, which is not zero.
Hence, no value of $k$ can make the matrix diagonal.
Final Answer: No value of $k$ makes the matrix diagonal.
Q18
2023
00:00
If $A = \begin{bmatrix}k & 0 \\ 0 & k\end{bmatrix}$ is an identity matrix, find $k$.
For an identity matrix, diagonal elements must be 1.
So $k = 1$.
Final Answer: $k = 1$