If $\begin{vmatrix} 1 & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2a \end{vmatrix} = 86$, then product of all values of $a$ is:

If $M = \begin{bmatrix} 2 \\ -1 \\ 3 \end{bmatrix}$ and $N = [7 \quad 1 \quad -4]$, then $(MN)^T$ will be equal to:

If $\begin{vmatrix} 2+x & y & z \\ x & 2+y & z \\ x & y & 2+z \end{vmatrix} = 0$, then the value of $x+y+z$ is

If $\begin{vmatrix} 2x & 5 \\ 8 & x \end{vmatrix} = \begin{vmatrix} 3 & 0 \\ 4 & -8 \end{vmatrix}$, then value(s) of x is/are

The number of diagonal matrices of order 3 with elements either 1 or 2, is:

Let $A$ and $B$ be two non-singular, square matrices of same order, and

A. $(AB)^{-1} = B^{-1} \cdot A^{-1}$

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

C. $adj. A = |A| \cdot A^{-1}$

D. $det(A^{-1}) = [det A]^{-1}$

Choose the correct answer from the options given below

If a matrix has 8 elements then the possible order(s) it may have

(A) $8 \times 1$

(B) $5 \times 3$

(C) $6 \times 2$

(D) $2 \times 4$

Choose the correct answer from the options given below: