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

Let $A=\left\{X=(x, y, z)^{T}: P X=0\right.$ and $\left.\mathrm{x}^{2}+\mathrm{y}^{2}+\mathrm{z}^{2}=1\right\}$ where $\mathrm{P}=\left[\begin{array}{ccc}1 & 2 & 1 \\ -2 & 3 & -4 \\ 1 & 9 & -1\end{array}\right]$ then the set $\mathrm{A}$ 

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

The matrix $A = \left[ {\begin{array}{*{20}{c}}{1/\sqrt 2 }&{1/\sqrt 2 }\\{ – 1/\sqrt 2 }&{ – 1/\sqrt 2 }\end{array}} \right]$ is