(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

1) Let A be an n x n matrix with A^2 -4A +5I = 0. Show that n must be even.

2) Let A be an m x n matrix where m<n. Show that det(A^{T}x A) = 0

3. The attempt at a solution

1) (A-2I)^2 +I=0

Not sure what to do after this though

Thanks in advance

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# A matrix satisfies A^2 - 4A + 5I = 0, then n is even.

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