# Math Help - Matrix Inverses.

1. ## Matrix Inverses.

Suppose that CA=I where C is m*n and A is n*m. Consider the system A.X=B of n equations in m variables.
Show that this system has a unique solution CB if it is consistent.
(Problem 11 a, page 60. "Linear Algebra with applications"-5th edition W. Keith
Nicholson)

2. Originally Posted by Bugati
Suppose that CA=I where C is m*n and A is n*m. Consider the system A.X=B of n equations in m variables.
Show that this system has a unique solution CB if it is consistent.
(Problem 11 a, page 60. "Linear Algebra with applications"-5th edition W. Keith
Nicholson)

$AX=B\,\,\,consistent\,\Longrightarrow\,CAX=CB\Long rightarrow I_mX=X=CB$ and since the system is consistent then X is uniquely determined by the product $CB$ and is thus unique.