Question

If the characteristic polynomial of a matrix A is p(λ) = λ²+ 1, then A is invertible

Answer 1

P($\lambda$ )=$\lambda$ ²+1$\implies$ $\exist$ A^-1

det(A-$\lambda$ E)=$\begin{vmatrix} - \lambda& 1 \\ -1 & - \lambda \end{vmatrix}$=P($\lambda$ )

$A=\begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$

detA=1 don`t equal 0$\implies\exist$ A^-1