Let A = [a_ij]_(2 x 4) and B = [b_ij]_(4 x 2), then, 3AB, is equal to Option 1: 3^2 AB Option 2: 3^4 AB Option 3: 3^2, A, B Option 4: 3^4, A, B

Answer: 3^2 AB. Solution: Matrix A is 2 x 4 (2 rows, 4 columns) Matrix B is 4 x 2 (4 rows, 2 columns) When multiplying AB: (2 x 4) x (4 x 2) = 2 x 2 matrix Since AB gives a 2 x 2 matrix, which is a square matrix, the determinant, AB, exists. Matrix A is 2 x 4, which is not square, so, A, does not exist. Matrix B is 4 x 2, which is not square, so, B, does not exist. For any n x n matrix M and scalar k:, kM, = k^n, M, where n is the size of the square matrix. AB is a 2 x 2 matrix, so n = 2 Scalar k = 3, 3AB, = 3^2, AB, 3AB, = 9, AB, The power depends on the final matrix size after multiplication, not the intermediate dimensions. Therefore, 3AB, = 9, AB, = 3^2, AB

Algebra

Matrices & Determinants

Medium

core

Let $A = [a_{ij}]_{2 \times 4}$ and $B = [b_{ij}]_{4 \times 2}$ , then $|3AB|$ is equal to

$3^2|AB|$

$3^4|AB|$

$3^2|A||B|$

$3^4|A||B|$

✅ Correct Option: 1

Matrix $A$ is $2 \times 4$ (2 rows, 4 columns)

Matrix $B$ is $4 \times 2$ (4 rows, 2 columns)

When multiplying $AB$ :

$(2 \times 4) \times (4 \times 2) = 2 \times 2$ matrix

Since $AB$ gives a $2 \times 2$ matrix, which is a square matrix, the determinant $|AB|$ exists.

Matrix $A$ is $2 \times 4$ , which is not square, so $|A|$ does not exist.

Matrix $B$ is $4 \times 2$ , which is not square, so $|B|$ does not exist.

For any $n \times n$ matrix $M$ and scalar $k$ :

$|kM| = k^n|M|$

where $n$ is the size of the square matrix.

$AB$ is a $2 \times 2$ matrix, so $n = 2$

Scalar $k = 3$

$|3AB| = 3^2|AB|$

$|3AB| = 9|AB|$

The power depends on the final matrix size after multiplication, not the intermediate dimensions.

Therefore, $|3AB| = 9|AB| = 3^2|AB|$

2025: 26 May Shift 2

If $A = \begin{bmatrix} x+z & 2 & -3 \\ x & 0 & 4 \\ 3 & x-y & 0 \end{bmatrix}$ is a skew-symmetric matrix, then which of the following are true?

(A) $y > z > x$

(B) $x > y$

(D) $z > x$

Choose the correct answer from the options given below:

2026: 15 May Shift 1

If the system of equations $x - ky - z = 0, kx - y - z = 0, x + y - z = 0$ has a non-zero solution, then possible values of $k$ are

2026: 22 May Shift 1

If the matrix $A=\begin{bmatrix}0 & -1 & 3x\\1 & y & -5\\-6 & 5 & 0\end{bmatrix}$ is skew-symmetric, then the value of $(5x-y)$ 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:

2023: 30 May Shift 3

If matrix $A = \begin{bmatrix} 3 & x \\ y & 0 \end{bmatrix}$ and $A' = A$ , then :

2026: 22 May Shift 1

If A is a square matrix such that $A^2=A$ and $I$ is identity matrix of same order, then $(2I+A)^3-19A$ is equal to:

Let A=[aij]2×4A = [a_{ij}]_{2 \times 4}A=[aij​]2×4​ and B=[bij]4×2B = [b_{ij}]_{4 \times 2}B=[bij​]4×2​, then ∣3AB∣|3AB|∣3AB∣ is equal to

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

Let $A = [a_{ij}]_{2 \times 4}$ and $B = [b_{ij}]_{4 \times 2}$ , then $|3AB|$ is equal to