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Sequences & Series

Let $true$ be the $4 \times 4$ real matrix

$\left[\begin{array}{cccc} 1 & 1 & 0 & 0 \\ -1 & -1 & 0 & 0 \\ -2 & -2 & 2 & 1 \\ 1 & 1 & -1 & 0 \end{array}\right]$

Then the characteristic polynomial for A is:

$x(x-1)^{2}$

$x^{2}(x+1)^{2}$

None of the above

$(x-1)^{2}(x+1)^{2}$