$A = [a_{ij}]_{m \times n}$ is a square matrix,if

For matrices $A$ and $B$,$A^{\prime} = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ and $B^{\prime} = \begin{bmatrix} 4 & 3 & 2 \end{bmatrix}$,then $(BA)^{\prime}$ is . . . . . . .

If $A = \begin{bmatrix} 3 & 4 \\ 1 & -6 \end{bmatrix}$ and $B = \begin{bmatrix} -2 & 5 \\ 6 & 1 \end{bmatrix}$, then find $X$ such that $A + 2X = B$.

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

For $3 \times 3$ order matrices $A$ and $B$,which of the following is generally true?

Find $X$ and $Y$,if $X+Y=\left[\begin{array}{ll}7 & 0 \\ 2 & 5\end{array}\right]$ and $X-Y=\left[\begin{array}{ll}3 & 0 \\ 0 & 3\end{array}\right]$.