If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$, then $A^2 - 5A$ is equal to : (where $I_2$ is identity matrix of order 2)

Match List - I with List - II.

Choose the correct answer from the options given below :

The real value of $a$ for which the system of equations $x+ay=0, y+az=0, z+ax=0$ has infinitely many solutions, is :

If $\begin{vmatrix}4x & 9\\ -4 & -5\end{vmatrix}=\begin{vmatrix}4 & 8\\ 2 & 3\end{vmatrix}$, then the value of $x$ is :

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:

If $A=\begin{bmatrix}x+4 & 3\\2 & 1\end{bmatrix}, B=\begin{bmatrix}5 & 2x-1\\2 & x\end{bmatrix}$ and $\lvert adj(AB) \rvert=32$, then the value of x is:

If $\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix}$, where a, b and c are non zero constants, then the value of $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$ is