# Math Help - matrices and determinants

1. ## matrices and determinants

Let A be an n x n matrix with A^2 - 4A + 5I=0?

show that n must be even.
it know you have to complete the square and take determinants but not sure how to do it

thanks

2. Originally Posted by b0mb3rz

Let A be an n x n matrix with A^2 - 4A + 5I=0. show that n must be even.

it know you have to complete the square and take determinants but not sure how to do it

thanks
we have $(A-2I)^2=-I$ and thus: $(\det(A - 2I))^2=(-1)^n.$ i think you can finish the proof now.