Algebra

Matrices & Determinants

Easy

applied

Let $A = [a_{ij}]$ be a square matrix of order 3 with each entry either 0 or 1, then the number of all such possible matrices is:

256

243

512

✅ Correct Option: 4

A 3×3 matrix has the form:

[a₁₁  a₁₂  a₁₃]
[a₂₁  a₂₂  a₂₃]
[a₃₁  a₃₂  a₃₃]

The total number of entries in a square matrix of order 3 is:

$3 \times 3 = 9$ entries

Each entry $a_{ij}$ can be filled in exactly 2 ways: either 0 or 1.

Since there are 9 entries and each entry has 2 independent choices:

Total number of possible matrices $= 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$

$= 2^9$

$= 512$

For an $n \times n$ matrix where each entry has $k$ choices:

Total matrices $= k^{n^2}$

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

Total $= 2^{3^2}$

$= 2^9$

$= 512$

Therefore, the number of all such possible matrices is 512.

2025: 3 June Shift 2

If $A = \begin{bmatrix} 5 & 2 \\ 4 & 3 \end{bmatrix}$ is a given matrix, then which of the following statements are correct?

(A) $|A| = 7$

(B) minor of $3 = -5$

(D) $adj(A) = \begin{bmatrix} 3 & -2 \\ -4 & 5 \end{bmatrix}$

Choose the correct answer from the options given below:

2026: 29 May Shift 1

If A is a non-singular matrix of order 3, then

Match List-I with List-II

List-I	List-II
Determinant of A	$\left\vert \text{adj}(\text{adj } A) \right\vert =$
(A) $\left\vert A \right\vert = 3$	(I) $1$
(B) $\left\vert A \right\vert = 4$	(II) $16$
(C) $\left\vert A \right\vert = 2$	(III) $81$
(D) $\left\vert A \right\vert = 1$	(IV) $256$

Choose the correct answer from the options given below:

2025: 21 May Shift 1

If A is a square matrix of order 3 such that $A( {adj } A) = \begin{bmatrix} -2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ , then $|A|$ is equal to

2026: 15 May Shift 1

Let P be a matrix such that $P = \begin{bmatrix} 1 & -1 \\ 0 & 3 \end{bmatrix}$ , then which of the following statements are True?

A. P is a symmetric matrix

B. P is not a skew-symmetric matrix

C. The determinant of P is non-zero

D. P is an invertible matrix

Choose the correct answer from the options given below:

2026: 29 May Shift 2

If $\begin{vmatrix}x&2\\18&x\end{vmatrix} = \begin{vmatrix}6&2\\18&6\end{vmatrix}$ , then x equals:

2026: 25 May Shift 1

Which of the following statements are TRUE?

A. If the product of two matrices is a zero matrix, it is not necessary that one of the matrix is a zero matrix.

B. For any three matrices A, B and C, $(AB)C = A(CB)$ .

C. Diagonal elements of a skew symmetric matrix can be non-zero.

D. Multiplication of diagonal matrices of same order is always commutative.

Choose the correct answer from the options given below:

Let A=[aij]A = [a_{ij}]A=[aij​] be a square matrix of order 3 with each entry either 0 or 1, then the number of all such possible matrices is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Let $A = [a_{ij}]$ be a square matrix of order 3 with each entry either 0 or 1, then the number of all such possible matrices is: