Determinants
Exercise 4.4.15
For the matrix \(A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & -3 \\ 2 & -1 & 3 \end{bmatrix}\), show that \(A^3 - 6A^2 + 5A + 11I = O\). Hence, find \(A^{-1}\).
For the matrix \(A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & -3 \\ 2 & -1 & 3 \end{bmatrix}\), show that \(A^3 - 6A^2 + 5A + 11I = O\). Hence, find \(A^{-1}\).