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 skew- symmetric matrix of odd order, then $ |A| $ is equal to

If $\mathrm{A}=\left[\begin{array}{c}-2 \\ 4 \\ 5\end{array}\right], \mathrm{B}=\left[\begin{array}{lll}1 & 3 & -6\end{array}\right],$ verify that $(\mathrm{AB})^{\prime}=\mathrm{B}^{\prime} \mathrm{A}^{\prime}$.

If  $A=\left[\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha\end{array}\right],$ then verify that $A^{\prime} A=I$

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: