Question

A = \(\begin{bmatrix} 2& -1 & +1 \\[0.3em] -1 & 2 &-1 \\[0.3em] 1 &-1 &2 \end{bmatrix}\), verify that A³ – 6A² + 9A – 4I = 0. find A^-1

Answer 1

A² = A x A

hence A³ - 6A² + 9A - 4I = 0