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 $\mathrm{A}$ 

For $a $ matrix  $ A, AI = A $ and $A{A^T} = I$is true for

Which one of the following is correct

If $A = \left[ {\begin{array}{*{20}{c}}1&2&3\\5&0&7\\6&2&5\end{array}} \right]$and $B = \left[ {\begin{array}{*{20}{c}}1&3&5\\0&0&2\end{array}} \right]$, then which of the following is defined

Let $A$ be a square matrix such that $A A^T=I$. Then $\frac{1}{2} A\left[\left(A+A^T\right)^2+\left(A-A^T\right)^2\right]$ is equal to