Mathematics - Matrices Question with Solution | TestHub

$A^2=\mathrm{I}$

$\Rightarrow A{A}^{\text{'}}=I$ (as $A^{\text{'}}=A$)

$\Rightarrow A$ is orthogonal

So, $x^2+y^2+z^2=1$ and $xy+yz+zx=0$

$\Rightarrow {\left(x+y+z\right)}^2=1+2\times 0$

$\Rightarrow x+y+z=1$

Thus, 

$x^3+y^3+z^3=3\times 2+1\times \left(1-0\right)$

$= 7$