If $\mathrm{A}^{\prime}=\left[\begin{array}{cc}3 & 4 \\ -1 & 2 \\ 0 & 1\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{ccc}-1 & 2 & 1 \\ 1 & 2 & 3\end{array}\right],$ then verify that  $(\mathrm{A}+\mathrm{B})^{\prime}=\mathrm{A}^{\prime}+\mathrm{B}^{\prime}$

Let $A$ be a square matrix of order $2$ such that $|A|=2$ and the sum of its diagonal elements is $-3$ . If the points $(x, y)$ satisfying $A^2+x A+y I=0$ lie on a hyperbola, whose transverse axis is parallel to the x-axis, eccentricity is e and the length of the latus rectum is $\ell$, then $\mathrm{e}^4+\ell^4$ is equal to……………………… 

Let $A=I_2-2 \mathrm{MM}^{\mathrm{T}}$, where $\mathrm{M}$ is real matrix of order $2 \times 1$ such that the relation $M^T M=I_1$ holds. If $\lambda$ is a real number such that the relation $\mathrm{AX}=\lambda \mathrm{X}$ holds for some non-zero real matrix $X$ of order $2 \times 1$, then the sum of squares of all possible values of $\lambda$ is equal to:

If $A',B'$ are transpose matrices of the square matrices $A,B$ respectively , then $(AB)'$is equal to

If matrix $A = {\left[ {{a_{ij}}} \right]_{3 \times 3}} , B = {\left[ {{b_{ij}}} \right]_{3 \times 3}}$ , where $a_{ij} + a_{ji} = 0$ and $b_{ij} -b_{ji} = 0\, \forall\, i , j$ then $A^4B^3$ is