For square matrices \(A,B\) and \(n\ge2\), \(A^n=B^n\) does not imply \(A=B\). In \(\Mat_2(\RR)\), let \[ M=\matt 0 1 1 0 . \] Then \(M^2=I=I^2\), but \(M\ne I\).
Does $A^n=B^n$ imply $A=B$?
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FE-W56LS$A^n = B^n$ does not imply $A = B$ for matricesvariant-of