Let A is a 4x4 matrix such that
A(0,1,0,1)^t=(0,1,0,1)^t and
A(1,0,1,0)^t=(-1,0,-1,0)^t. Also, suppose A has trace 4 and det 9/4.
Find all eigenvalues of A and their multiplicites and explain why (1,1,1,1) is not an eigenvector of A.

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**the determinant is the product of the eigenvalues

All i'm confused about it the information at the beginning

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