Matrix problem

You assumed that A is an invertible matrix

Ohh Thank you very much Alan!Have a nice day!

If it's not we can't prove Α^-1 = -Α^4 

You know the question better than me, are you supposed to assume that A is invertible? It IS possible to prove that A is invertible, so I don't think you're supposed to assume that.

First you must prove that,A is invertible because if it don't we can't prove Α^-1 = -Α^4

I know that, but I'm not going to give you the answer, I want you to try first

I think i know how to prove it im in 2nd year in Greek university in Math science but this is a lesson for 1st year 

and I'm doing it again!

Its -A^4 + A^3 - A^2 + A = I <=> 

<=> A( -A^3 + A^4 - A + I) =I 

so ( -A^3 + A^4 - A + I)=A^-1

Yes I think you got it, But just to be sure:

You got the equation A*(-A³+A²-A¹+I)=I. We can replace -A³+A²-A¹+I with "B". So we got A*B=I. I is an invertible matrix, and if a multiplication of two matrices results in an invertible matrix this means that both matrices are also invertible, meaning that A is invertible.

Yes exactly from definition of  invertible matrix!

Thanks guys for your tips!