Algebra

Matrices & Determinants

Easy

applied

The number of all possible matrices of order $2 \times2$ with each entry $0, 1$ or $2$ are.

✅ Correct Option: 2

A 2×2 matrix has 4 positions arranged in 2 rows and 2 columns:

[a  b]
[c  d]

There are 4 entries to fill.

Each entry can be filled with 0, 1, or 2.

This gives 3 choices for each entry.

The choices for each entry are independent:

Entry $a$ : 3 choices

Entry $b$ : 3 choices

Entry $c$ : 3 choices

Entry $d$ : 3 choices

Total number of matrices $= 3 \times 3 \times 3 \times 3$

$= 3^4$

$= 81$

For an $m \times n$ matrix with $k$ choices per entry:

Total matrices $= k^{m \times n}$

Here: $k = 3$ , $m = 2$ , $n = 2$

Total matrices $= 3^{2 \times 2} = 3^4 = 81$

2026: 19 May Shift 1

If A is a 3-rowed square matrix and $|A| = 5$ , then $|adjA|$ is equal to

2025: 2 June Shift 1

The matrix $A = \begin{bmatrix}0 & 0 & 5\\0 & 5 & 0\\5 & 0 & 0\end{bmatrix}$ is a

(A) Diagonal matrix

(B) Scalar matrix

(D) Symmetric matrix

Choose the correct answer from the options given below:

2026: 30 May Shift 2

If $A = \begin{bmatrix}0 & x & 3\\2 & y & -1\\z & 1 & 0\end{bmatrix}$ is a skew-symmetric matrix, then the value of $3x+y-2z$ is

2026: 22 May Shift 2

Match List-I with List-II

List-I	List-II
(A) If $A = [a_{ij}]_{n \times n}$ , where $a_{ij} = \begin{cases}0, & i \ne j \\ k, & i=j, k\ne 0\end{cases}$ then A is ___	(I) Symmetric matrix
(B) If $A = [a_{ij}]_{2\times 2}$ , where $a_{ij} = \begin{cases}1, & i \ne j \\ 0, & i=j\end{cases}$ , then $A^2$ is ___	(II) Skew-Symmetric matrix
(C) If A and B are matrices of the same order, then $(AB^T - BA^T)$ is ___	(III) Identity matrix
(D) If A and B are symmetric matrices of the same order, then $(AB+BA)$ is ___	(IV) Scalar matrix

Choose the correct answer from the options given below:

2026: 14 May Shift 2

If A is a 3x3 matrix then:

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\vert adj A\vert$	I.	$\vert A\vert^{-1}$
B.	$\vert A.adj A\vert$	II.	$\vert A\vert$
C.	$\vert A^{-1}\vert$	III.	$\vert A\vert^2$
D.	$\vert A^{-1}.adj A\vert$	IV.	$\vert A\vert^3$

Choose the correct answer from the options given below:

2025: 22 May Shift 2

Consider the matrices $A = \begin{bmatrix} 9 & 0 & 0 \\ 0 & 16 & 0 \\ 0 & 0 & 25 \end{bmatrix}$ and $B = \begin{bmatrix} \frac{1}{5} & 0 & 0 \\ 0 & \frac{1}{4} & 0 \\ 0 & 0 & \frac{1}{3} \end{bmatrix}$ . The value of $|(AB)^{-1}|$ is

The number of all possible matrices of order 2×22 \times22×2 with each entry 0,10, 10,1 or 222 are.

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

The number of all possible matrices of order $2 \times2$ with each entry $0, 1$ or $2$ are.