# Powers of matrices equal to the identity matrix

by Bipolarity
Tags: equal, identity, matrices, matrix, powers
 P: 783 I am curious about under what conditions the powers of a square matrix can equal the identity matrix. Suppose that A is a square matrix so that $A^{2} = I$ 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
 P: 783 I see. Thanks much $\aleph_0$ BiP