I just finished a final in a linear algebra course and was unsure about one of the questions. The question was:(adsbygoogle = window.adsbygoogle || []).push({});

If A^2 - A + I = 0 , show that A is invertible.

My approach was that det(A^2 + I) = det(A)

det(A^2 + I) will never be zero, so det(A) is non-zero and therefore A is invertible.

Is this the right way of doing this problem?

Thanks!

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# Matrix invertibility question

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