If A is a diagonal matrix of order 3 with diagonal elements as 2, 3, 4, then |adj A| is

Let A be a square matrix of order 2 such that $\begin{bmatrix} 2 & 1 \\ 3 & 2 \end{bmatrix} A \begin{bmatrix} -3 & 2 \\ 5 & -3 \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, then A is:

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

Let A = [aᵢⱼ]ₙₓₙ and B = [bᵢⱼ]ₙₓₙ. Then which of the following is/are true?

(A) AB = BA

(B) (AB)⁻¹ = B⁻¹ A⁻¹

(C) $(AB)^T = B^T A^T$

(D) AB = 0 ⇒ A = 0 or B = 0

Choose the correct answer from the options given below:

The breadth of plot is:

Which of the given values of $x$ and $y$ make the following pair of matrices equal ?

$\begin{bmatrix}2x-1 & 4\\y-1 & 3+2x\end{bmatrix}$ and $\begin{bmatrix}0 & y-2\\5 & 4\end{bmatrix}$

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: