Let A be a square matrix of order 3 and I is an identity matrix of order 3. If $|A| = 3$, the value of $|A(4I)|$ is

For the system of equations AX = B, which of the following is correct?

If $A$ and $B$ are square matrices of the same order, then which of the following statements are correct?

(A) $|A^{-1}| = |A|^{-1}$

(B) $adj(A) = |A|A^{-1}$

(C) $(A + B)^{-1} = B^{-1} + A^{-1}$

(D) $(AB)^{-1} = B^{-1}A^{-1}$

Choose the correct answer from the options given below:

Assume A, B and C are matrices of order $m \times n$, $n \times 3$ and $3 \times q$ respectively. The restrictions on $_{m,n}$ and $_q$ so that $AB + BC$ is defined are

If A is a matrix of order $3 \times 3$ such that $|A| = 4$ and $|k \cdot adj\, A| = 32|A|, k \in \mathbb{R}$; then the value of k is:

If $\begin{bmatrix} x-2y & z \\ 3x+y & w \end{bmatrix}=\begin{bmatrix} 1 & 2 \\ -11 & 1 \end{bmatrix}$; then the value of $y-x$ is:-

If matrix A is of order $2 \times 3$ and B of order $3 \times 2$, then