If $A = \begin{bmatrix} 1 & 2 \\ -3 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} -1 & 0 \\ 2 & 3 \end{bmatrix}$,then:

Suppose $A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$ is a real matrix with non-zero entries,$ad - bc = 0$ and $A^2 = A$. Then,$a + d$ equals

If $A = \begin{bmatrix} 4 & 2 \\ -1 & 1 \end{bmatrix}$ and $I$ is the identity matrix of order $2$,then $(A - 2I)(A - 3I) = $

If $M$ is a $3 \times 3$ matrix such that $(0\,1\,2) M = (1\,0\,0)$ and $(3\,4\,5) M = (0\,1\,0)$, then $(6\,7\,8) M$ is equal to

Let $Q = \begin{bmatrix} \cos \frac{\pi}{4} & -\sin \frac{\pi}{4} \\ \sin \frac{\pi}{4} & \cos \frac{\pi}{4} \end{bmatrix}$ and $x = \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{bmatrix}$. Then $Q^{3} x$ is equal to:

$A$ square matrix $[a_{ij}]$ in which $a_{ij} = 0$ for $i \neq j$ and $a_{ij} = k$ (constant) for $i = j$ is called a