Let A be the 4 × 4 real matrix i.e. A = \( \begin{bmatrix} {1} & {1} & 0 &0\\[0.3em] -1 & -1 & 0&0 \\[0.3em] -2& -2& 2&0 \\[0.3em] 1 &1&-1&0 \end{bmatrix} \). Then the characteristic polynomial for A is
1
x2(x - 1)2
2
x2(x + 1)2
3
(x - 1)2(x + 1)2
4
2x2 - 1