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) ?

This video may be helpful: https://www.youtube.com/watch?v=gVF4F74Scf8 — Math1000, Nov 02 '19 at 14:40

score 1 · Answer 1 · answered Nov 02 '19 at 13:33

1

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

answered Nov 02 '19 at 13:33

Bernard

1 Answers1