Question

Let A and B be 5x5 matrices, such that B is invertible. Suppose that AB = BA.Show that A is not invertible.

Answer 1

i think it has someting to do with left or right multiplication of the inverses; but i cant see it

Answer 2

abb' = bab'

a = bab'

aa' = bab'a'

i = bab'a'

b' = ab'a'

b'a = ab'

yeah, i cant see it