What are the values of $(x, y, z, t)$,if $3\begin{bmatrix} x & y \\ z & t \end{bmatrix} = \begin{bmatrix} x & 6 \\ -1 & 2t \end{bmatrix} + \begin{bmatrix} 4 & x+y \\ z+t & 3 \end{bmatrix}$?

Consider the matrices $A = \begin{bmatrix} 4 & 6 & -1 \\ 3 & 0 & 2 \\ 1 & -2 & 5 \end{bmatrix}$,$B = \begin{bmatrix} 2 & 4 \\ 0 & 1 \\ -1 & 2 \end{bmatrix}$,and $C = \begin{bmatrix} 3 \\ 1 \\ 2 \end{bmatrix}$. Which of the following matrix products are defined?
$(i) (AB)^T C$
$(ii) C^T C (AB)^T$
$(iii) C^T AB$
$(iv) A^T AB B^T C$

If $A$ and $B$ are two matrices such that $AB$ is an identity matrix and the order of matrix $B$ is $3 \times 4$,then the order of matrix $A$ is

If $A = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 2 & 3 & 0 & 0 \\ 4 & 5 & 6 & 0 \\ 7 & 8 & 9 & 10 \end{bmatrix}$,then $A$ 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 $A = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$,then $(A+I)^3 + (A-I)^3 = \dots$