Proving Properties of Non-Square Matrices

[mathguy34]

I need help proving the following:

1 A non-square matrix cannot have both a left and a right inverse
2 If a non-square matrix has a left(right) inverse, it has infinitely many.
3 If m<n, a non-square matrix has a right inverse if and only if rank A=m

 

[ice109]

I need help proving the following:

1 A non-square matrix cannot have both a left and a right inverse
2 If a non-square matrix has a left(right) inverse, it has infinitely many.
3 If m<n, a non-square matrix has a right inverse if and only if rank A=m

construct a non square matrix and try to find its inverse and see what happens.

 

[mathguy34]

Okay

Okay, but how does that show point 1 and 3