Matrix Equation Inverse

Question

How can I show that if a square matrix A satisfies: (A^2) - 4A + 3I = 0 (where “I” is the identity matrix) then: (A^-1) = (1/3)(4I - A) ?

Answer 1

Rewrite the equation as $$3I=4A-A^2=A(4I-A).$$