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

Is the following matrix a perfect square? A matrix A is a perfect square if there is a matrix B such that A = B^{2}

____1 1 0 0

A = 0 1 0 0

-----0 0 1 0

-----0 0 0 1

2. Relevant equations

3. The attempt at a solution

I haven't come across anything like this before, but here's what I'm thinking.

All eigenvalues of A are equal to 1, and the minimal polynomial is m(t) = (t-1)^{2}

and the characteristic polynomial is p(t) = (t-1)^{4}.

Both of these are perfect squares, so does that mean the matrix is a perfect square?

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# Matrix is a perfect square?

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