Prove Vector Equations: AB=Im & m<=n

[daniel_i_l]

Homework Statement

A is a mxn matrix and B is a nxm matrix. AB = Im.
a) Prove that there's only one solution to Bx = 0 where x and 0 are coloum vectors.
b) Prove that m<=n

Homework Equations

if A is a mxn n>m then there're infinite solutions to Ax=0

The Attempt at a Solution

a) Bx=0 => ABx=A0 => Ix=0 => x=0 so there's only the trivial solution.
b) according to the equation above if m>n then there would be an infinite amount of solutions to Bx=0 and not only one.
Did I do that right? This was a problem on an exam and it relative to the other questions it looks to easy.

 

[radou]

Hm, looks okay.