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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: enter image description here

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!!!

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Hint:

\begin{align} (PQP^{-1})^2= PQP^{-1}PQP^{-1} = PQIQP^{-1} = PQ^2P^{-1}. \end{align}

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  • $\begingroup$ how did you get I? $\endgroup$ – ISuckAtMathPleaseHELPME Oct 30 '16 at 0:41
  • $\begingroup$ What is $P*P^{-1}$? $\endgroup$ – Jacky Chong Oct 30 '16 at 0:52

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