If $\begin{bmatrix} 2 & 3 & 4 \end{bmatrix} \begin{bmatrix} 1 & x & 3 \\ 2 & 4 & 5 \\ 3 & 2 & x \end{bmatrix} \begin{bmatrix} x \\ 2 \\ 0 \end{bmatrix} = O$,then $x = $ . . . . . .

If $A$ and $B$ are two matrices,such that $AB = B$ and $BA = A$,then $A^2 + B^2$ is equal to:

If $A=\left[\begin{array}{lll}9 & 3 & 0 \\ 1 & 5 & 8 \\ 7 & 6 & 2\end{array}\right]$ and $AA^T-A^2=\left[\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right]$, then $\sum_{\substack{1 \leq i \leq 3 \\ 1 \leq j \leq 3}} a_{i j}=$

If $A$ is a $2 \times 2$ matrix and $a_{ij} = \frac{i + 2j^2}{3}$,then find the matrix $A = [a_{ij}]_{2 \times 2}$.

If $A = \begin{bmatrix} i & 0 \\ 0 & -i \end{bmatrix}$ and $B = \begin{bmatrix} 0 & i \\ i & 0 \end{bmatrix}$,where $i = \sqrt{-1}$,then which of the following relations is correct?

If $A = \begin{bmatrix} \alpha & 0 \\ 1 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 \\ 5 & 1 \end{bmatrix}$,then the value of $\alpha$ for which $A^2 = B$ is: