Let $A=[a_{ij}]$ be a matrix of order $3 \times 4$ such that $a_{ij}=\begin{cases}2i-3j, & i \ge j \\ 3i+j, & i<j\end{cases}$ then the sum of all the elements of the first two rows of this matrix is:

The integral value of k for which the system of linear equations $kx + y + 2z = 0$, $ky = x - 3z$ and $2x + y + kz = 0$ has a non-zero solution is

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 $\begin{vmatrix}2a & 2a & 3b+c\\3b & 2a+c & 3b\\2a+3b & c & c\end{vmatrix} = 48$, then abc is equal to

If the system of equation

$x - y + z = 4$

$x - 2y - 2z = 9$

$2x + y + \lambda z = 1$

has a unique solution, then

If $A = \begin{bmatrix} 1 & 2 & -3 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 3 \\ 7 & -8 \\ 1 & 2 \end{bmatrix}$, then which of the following are true?

(A) AB is a $2 \times 3$ matrix

(B) $B^2$ is a $3 \times 3$ matrix

(C) BA is not possible

(D) $A^3$ is not possible

Choose the correct answer from the options given below:

Let $I = \begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}$ and $A = \begin{bmatrix}1 & -2\\2 & 4\end{bmatrix}$ be two matrices such that $8A^{-1} = kI - A, k \in \mathbb{R}$, then the value of $k$ is: