Prove a matrix is invertible The $2 \times 2$ matrix ${A}$ satisfies
$A^2 - 4 {A} - 7{I} = {0},$
where ${I}$ is the $2 \times 2$ identity matrix. Prove that ${A}$ is invertible.
What is the best way to do this?

$${1\over7}(A-4I)A={1\over 7}(A^2-4A)={1\over 7}{7I}=I\\
A{1\over7}(A-4I)={1\over 7}(A^2-4A)={1\over 7}{7I}=I$$
