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

If $A = [1, 2, 3]$,$B = \begin{bmatrix} 2 \\ 3 \\ 4 \end{bmatrix}$ and $C = \begin{bmatrix} 1 & 5 \\ 0 & 2 \end{bmatrix}$,then which of the following is defined?

If $A = \begin{bmatrix} 1 & 2 & 3 \\ 5 & 0 & 7 \\ 6 & 2 & 5 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 3 & 5 \\ 0 & 0 & 2 \end{bmatrix}$,then which of the following is defined?

The identity element in the group $M = \left\{ \begin{bmatrix} x & x \\ x & x \end{bmatrix} \mid x \in \mathbb{R}, x \neq 0 \right\}$ with respect to matrix multiplication is

$A=\left[\begin{array}{ccc}a^2 & 15 & 31 \\ 12 & b^2 & 41 \\ 35 & 61 & c^2\end{array}\right]$ and $B=\left[\begin{array}{ccc}2 a & 3 & 5 \\ 2 & 2 b & 8 \\ 1 & 4 & 2 c-3\end{array}\right]$ are two matrices such that the sum of the principal diagonal elements of both $A$ and $B$ are equal,then the product of the principal diagonal elements of $B$ is

If $A = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}$ and $\theta = \frac{2 \pi}{7}$, then $A^{100} = A \times A \times \dots \times A$ ($100$ times) is equal to: