Suppose A^k=0 for some integer k is greater than or equal to 1

[Chris Rorres]

I was wondering if anyone could give me some hints on this

Suppose A^k=0 for some integer k is greater than or equal to 1. Prove that A is not invertible.

 

[VeeEight]

Try a proof by contradiction. Assume it is invertible with inverse B. Then AB=1. (A^k)B=0B=0
But B=A^-1. So you can simplify (A^k)B=(A^k)(A^-1)=...

 

[HallsofIvy]

Nice!