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 $A=\left[\begin{array}{lll}3 & \sqrt{3} & 2 \\ 4 & 2 & 0\end{array}\right]$ and $B=\left[\begin{array}{rrr}2 & -1 & 2 \\ 1 & 2 & 4\end{array}\right],$ verify that $\left(\mathrm{A}^{\prime}\right)^{\prime}=\mathrm{A}$.

Given $A =$$\left[ {\begin{array}{*{20}{c}}1&3\\2&2\end{array}} \right]$ ; $I =$$\left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right]$ . $If A – \lambda I$ is a singular matrix then

If  $A$  is a square matrix for which ${a_{ij}} = {i^2} – {j^2}$, then $A$ is

The total number of matrices $A = \left[ {\begin{array}{*{20}{c}}
0&{2x}&{2x}\\
{2y}&y&{ – y}\\
1&{ – 1}&1
\end{array}} \right];\,\left( {x,y \in R,\,x \ne y} \right)$ for which ${A^T}A = 3{I_3}$