Let $A = \begin{bmatrix} x & 1 \\ 1 & 0 \end{bmatrix}$,$x \in \mathbb{R}$ and $A^{4} = [a_{ij}]$. If $a_{11} = 109$,then $a_{22}$ is equal to

$A$ square matrix $[a_{ij}]$ in which $a_{ij} = 0$ for $i \neq j$ and $a_{ij} = k$ (constant) for $i = j$ is called a

If $A = \begin{bmatrix} 2 & -1 \\ -7 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 4 & 1 \\ 7 & 2 \end{bmatrix}$,then which of the following is correct?

If $I$ is the identity matrix of order $2$ and $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$, then for $n \geq 1$, mathematical induction gives:

If $P = \begin{bmatrix} \cos \frac{\pi}{4} & -\sin \frac{\pi}{4} \\ \sin \frac{\pi}{4} & \cos \frac{\pi}{4} \end{bmatrix}$ and $X = \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{bmatrix}$, then $P^3 X$ is equal to:

If $A = \begin{bmatrix} i & 0 \\ 0 & i \end{bmatrix}$,then ${A^2} = $