from A2 + 5A + 6I = 0 we have:
6I = -A2 - 5A
I = (1/6)(-A - 5I)A
so evidently, A-1 = (-1/6)(A + 5I)
(not only is A invertible, we actually found the inverse!)
I need to prove that if then A is invertibale.
so im not sure if thats valid, but i think i can write it like that:
but it still doesn't prove that or , since they're bote can be zero divisors and therefore don't necessarily equal 0.
so im kinda lost here.
is there another way?