I am curious about under what conditions the powers of a square matrix can equal the identity matrix.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose that A is a square matrix so that [itex] A^{2} = I [/itex]

At first I conjectured that A is also an identity matrix, but I found a counterexample to this.

I noticed that the counterexample was an elementary matrix.

So then I conjectured that A is an elementary matrix. Is this true? Can I prove this? What about for general powers of A?

BiP

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# Powers of matrices equal to the identity matrix

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