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

In a third-order matrix $A$,$a_{ij}$ denotes the element in the $i$-th row and $j$-th column. If $a_{ij} = 0$ for $i = j$,$1$ for $i > j$,and $-1$ for $i < j$,then the matrix is:

If a matrix $A = \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}$ satisfies $A^6 = k A$,then the value of $k$ is

If $A = \begin{bmatrix} 2 & -3 \\ -4 & 1 \end{bmatrix}$,then $(A^T)^2 + (12 A)^T = $

Construct a $3 \times 4$ matrix,whose elements are given by $a_{i j}=\frac{1}{2}|-3 i+j|$.

For $A = \begin{bmatrix} 0 & 0 & 3 \\ 0 & 3 & 0 \\ 3 & 0 & 0 \end{bmatrix}$,which statement is correct?