Let . Then or . Now use this fact and the distributive law to show
. (You know this proves the statement, don't you?)
Hi, everyone ~
I read Linear Algebra by Hoffman & Kunze.
At 190pg #8,
A, B := n*n matrices . Prove that if I-AB is invertible, then I-BA is invertible and (I-BA)^(-1) = I +B(I-AB)^(-1) A.
Any hint or comment are welcomed !
Please help !