Determinants and Matrices — Maths STD 11 Science — Question

i.e, to prove $A^2+A B+B A+B^2=A^2+A B+B^2$,

i.e., to prove BA = 0.

$\begin{aligned} & B A=\left[\begin{array}{cc}5 & -4 \\ 10 & -8\end{array}\right]\left[\begin{array}{cc}8 & 4 \\ 10 & 5\end{array}\right] \\ & {\left[\begin{array}{ll}40-40 & 20-20 \\ 80-80 & 40-40\end{array}\right]=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]}\end{aligned}$