Mathematics - Matrices Question with Solution | TestHub

We get $A=A^T$.

Given $AB=I$ and $2A+3B{B}^T=I$, we also have $2A^T-3B{B}^T=I$.

From these, we deduce $A=A^T$.

Also, $|3B{B}^T|=|I-2A^T|=|I-2A|$.

This implies $27=|I-2A||A{|}^2=|A^2-2A^3|$.