assume that P and Q are both nxn matrices and that P is invertible. Prove by induction on k that for all k>=1 (k greater than equal to 1) we have:
Please need help... i am stuck i figured out the base case for k = 1 and then after that i do not know how to proceed!!!
Hint:
\begin{align} (PQP^{-1})^2= PQP^{-1}PQP^{-1} = PQIQP^{-1} = PQ^2P^{-1}. \end{align}