Let A be an n x n matrix with A^2 - 4A + 5I=0? show that n must be even. it know you have to complete the square and take determinants but not sure how to do it thanks
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Originally Posted by b0mb3rz Let A be an n x n matrix with A^2 - 4A + 5I=0. show that n must be even. it know you have to complete the square and take determinants but not sure how to do it thanks we have $\displaystyle (A-2I)^2=-I$ and thus: $\displaystyle (\det(A - 2I))^2=(-1)^n.$ i think you can finish the proof now.
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