- #1
bologna121121
- 9
- 0
Homework Statement
Prove in general that if m does not equal n, then AB and BA cannot both be identity matrices, where A is mxn and B is nxm.
Homework Equations
None (that I know of at least).
The Attempt at a Solution
At first I thought it would be a good idea to define each element in A and B and write out some elements from AB and BA, and hope that I noticed a pattern where I would see something possible only if n=m. This proved very cumbersome and I could not get it to go anywhere.
Next I tried assuming that both AB and BA equaled identity matrices of appropriate dimensions, with the intention of deriving a contradiction, but I was unfortunately unavle to do so.
I appreciate any help, as I really don't know what to try next.