# Invertible matrices

charlies1902
Let A and B be n × n matrices.
a. Show that if A is invertible and AB = 0, then
B = 0.

If A is invertible, it can be reduced to the I matrix.
Thus IB=0 (this is the part where I'm hesitant, can I say that IB=0?)
Thus B=0 since I≠0

Homework Helper
Gold Member
Let A and B be n × n matrices.
a. Show that if A is invertible and AB = 0, then
B = 0.

If A is invertible, it can be reduced to the I matrix.
Thus IB=0 (this is the part where I'm hesitant, can I say that IB=0?)
Thus B=0 since I≠0

How did you reduce A to the I matrix? What operation(s) did you perform?

charlies1902
How did you reduce A to the I matrix? What operation(s) did you perform?

Multiplying A^-1 to both sides. Is this necessary to state in the proof?

When I got the BI=0, I think I got it for the wrong reasons. I'm not very good at proofs. It took me awhile to think of multiplying A^-1 to both sides that that's how it justified BI=0. Typically when you go about doing proofs, how do you think in the "right" direction? Proofs seem to be so open ended compared to computation problems, that if you're not thinking in the "right" direction, it might take you a very long time to get it. Do you have any tips?