Mathematics - Matrices Question with Solution | TestHub

Let $A=\left[\begin{array}{cc}2& 0\\ 0& -3\end{array}\right]$, $B=\left[\begin{array}{cc}0& 1\\ 3& 0\end{array}\right]$ and $X=\left[\begin{array}{cc}\cos x& -\sin x\\ \sin x& \cos x\end{array}\right]$. If $P=AXB$,

$Q=BXA$ and $(Tr(PQ){)}^{10}=a^{10}+b^{10}$, where $a<b$, then find the value of $b-2a$. ($Tr(M)$ denotes the trace of Matrix $M$ and $M^{\mathsf{T}}$ denotes the transpose of matrix $M$).