The order of matrix $A$ is $m \times n$ and for matrix $B$,if $AB^{\prime}$ and $B^{\prime}A$ are defined,then the order of matrix $B$ is . . . . . . .

Construct a $2 \times 2$ matrix,$A = [a_{ij}]$,whose elements are given by $a_{ij} = \frac{i}{j}$.

If $A+2B = \begin{bmatrix} 1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1 \end{bmatrix}$ and $2A-B = \begin{bmatrix} 2 & -1 & 5 \\ 2 & -1 & 6 \\ 0 & 1 & 2 \end{bmatrix}$, then $\operatorname{tr}(A)-\operatorname{tr}(B) =$

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 $A = \begin{bmatrix} 3 & 3 & 3 \\ 3 & 3 & 3 \\ 3 & 3 & 3 \end{bmatrix}$,then $A^3 = $ . . . . . . (in $A$)

If $A=\left[\begin{array}{cccc}2 & 1 & 3 & -1 \\ 1 & -2 & 2 & -3\end{array}\right]$,$B=\left[\begin{array}{cccc}2 & 1 & 0 & 3 \\ 1 & -1 & 2 & 3\end{array}\right]$ and $2A+3B-5C=0$,then $C=$