If $A = \begin{bmatrix} 3 & 7 \\ 4 & -2 \end{bmatrix}$, $X = \begin{bmatrix} \alpha \\ -2 \end{bmatrix}$, $B = \begin{bmatrix} 7 \\ 32 \end{bmatrix}$ and $AX = B$, then the value of the $\alpha$ is

If A is a non-singular matrix of order 3, then

Match List-I with List-II

Choose the correct answer from the options given below:

Let $\begin{vmatrix} x & 2 \\ 18 & x \end{vmatrix} = \begin{vmatrix} -4 & -2 \\ -8 & -4 \end{vmatrix}$. Then

(A) $x = -4$

(B) $x = -6$

(C) $x = 4$

(D) $x = 6$

Choose the correct answer from the options given below:

If order of matrix A is $m \times p$ and order of matrix B is $p \times n$, then what is the order of matrix AB ?

If matrix $A = \begin{bmatrix} p & -3 \\ -4 & p \end{bmatrix}$ and $|A^3| = 64$, then the value of p is:

The inverse of the matrix $A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$ is:

Let $A = \begin{bmatrix} 2 & 4 \\ -2 & 8 \end{bmatrix}$. If $A^{-1} = \alpha I + \beta A$, $\alpha,\beta \in R$ (Where R is set of real numbers) and I is a $2\times2$ identity matrix, than the value of $4(\alpha-2\beta)$ is equal to: