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Homework Statement
Is the following matrix a perfect square? A matrix A is a perfect square if there is a matrix B such that A = B2
____1 1 0 0
A = 0 1 0 0
-----0 0 1 0
-----0 0 0 1
Homework Equations
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?