Can someone show me how to answer this question:

If a square matrix A satisfies A^5 − 4A + 5I = 0, which of the following is equal to A^−1 ?

Its been awhile since ive done this math and ive had a few drinks so i may be wrong here.

I believe you will need a diagonal matrix A with all numbers along the diagonal being equal.

so then you have

some number x that solves: x^5 - 4x + 5*1 = 0
which i think is ~ -1.63044 - plug that in for the diagonal along matrix A

then you would just have to find the inverse matrix.

A^5 - 4A = -5I
(-1/5)*(-5A^4 +20I)*A = I

which can be written as B*A = I, with B = (-1/5)*(-5A^4 + 20I)
which means (by definition) that A^-1 = B