. Is it possible to have AB=In without B being the inverse of A?

[madah12]

Homework Statement

30.
Is it possible to have AB= In without B being the inverse of A? Explain your reasoning.

Homework Equations

The Attempt at a Solution

yes if A=
|1 1 0|
|0 1 0|
B=

|1 -1|
|0 1|
|0 0|
AB=I(2) , BA=! I3 right?

 

[rock.freak667]

That would be true once A and B do not have the same dimensions (as you showed using an example)