Algebra

Matrices & Determinants

Easy

applied

The number of all possible matrices of order $2 \times 3$ with entries -1 or 1 is

✅ Correct Option: 1

A matrix of order $2 \times 3$ has 2 rows and 3 columns:

$\begin{bmatrix} \_ & \_ & \_ \\ \_ & \_ & \_ \end{bmatrix}$

Total number of entries $= 2 \times 3 = 6$

Each entry can be filled with either $-1$ or $1$ .

Each entry has 2 choices.

For 6 independent entries, each with 2 choices:

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

$= 2^6$

$= 64$

For any matrix with $n$ entries where each entry has $k$ choices:

Total possible matrices $= k^n$

Here: $k = 2$ , $n = 6$

Therefore: $2^6 = 64$

2026: 30 May Shift 2

If A and B are invertible matrices of the same order, then

Match List-I with List-II

List-I (Determinant)	List-II (Equal to)
(A) $\left\vert A^{-1}B \right\vert$	(I) $\dfrac{1}{\left\vert A \right\vert \left\vert B \right\vert}$
(B) $\left\vert AB^{-1} \right\vert$	(II) $\dfrac{\left\vert B \right\vert}{\left\vert A \right\vert}$
(C) $\left\vert A^{-1}B^{-1} \right\vert$	(III) $\left\vert A \right\vert \left\vert B \right\vert$
(D) $\left\vert AB \right\vert$	(IV) $\dfrac{\left\vert A \right\vert}{\left\vert B \right\vert}$

Choose the correct answer from the options given below:

2026: 26 May Shift 2

If $A = \begin{bmatrix} 1 & 0 \\ -1 & 7 \end{bmatrix}$ is a matrix such that $A^2 = 8A + KI$ ,where $I$ is an identity matrix of order 2 then value of $K$ is :

2026: 25 May Shift 1

For a square matrix $A$ of order 3, if $\lvert A\rvert = -3$ , then $\lvert 4\,adj A\rvert$ is equal to

2025: 13 May Shift 2

For the system $\begin{bmatrix} 2 & -3 \\ -4 & 6 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 5 \\ -10 \end{bmatrix}$ which of the following statements are correct?

(A) The system has no solution.

(B) The system is consistent.

(D) It has a unique solution.

Choose the correct answer from the options given below:

2026: 22 May Shift 2

If $A = \begin{bmatrix}0 & a & -3 \\ 2 & 0 & -1 \\ b & 1 & 0\end{bmatrix}$ is a skew-symmetric matrix, then

2025: 21 May Shift 1

If the matrix $A = \begin{bmatrix} 1 & 3 \\ 2 & 1 \end{bmatrix}$ , then the value of det $(A^2 - 2A)$ is equal to

The number of all possible matrices of order 2×32 \times 32×3 with entries -1 or 1 is

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The number of all possible matrices of order $2 \times 3$ with entries -1 or 1 is