Let $P $ and $Q $ be $3×3$ matrices $P \ne Q$. If ${P^3} = {Q^3},{P^2}Q = {Q^2}P$ then determinant of $\det \left( {{P^2} + {Q^2}} \right)$ is equal to :
$-2$
$1$
$0$
$-1$
The system of equations $kx + 2y\,-z = 1$ ; $(k\,-\,1)y\,-2z = 2$ ; $(k + 2)z = 3$ has unique solution, if $k$ is equal to
The sum of the real roots of the equation $\left| {\begin{array}{*{20}{c}}
x&{ - 6}&{ - 1}\\
2&{ - 3x}&{x - 3}\\
{ - 3}&{2x}&{x = 2}
\end{array}} \right| = 0$ is equal to
If $2x + 3y - 5z = 7, \,x + y + z = 6$, $3x - 4y + 2z = 1,$ then $x =$
Let $\left| {\,\begin{array}{*{20}{c}}{6i}&{ - 3i}&1\\4&{3i}&{ - 1}\\{20}&3&i\end{array}\,} \right| = x + iy$, then