Thread: 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

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 and thus: i think you can finish the proof now.