# Thread: 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)

Please help me!

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)

Please help me!

Well, the definition of consistency in that book is precisely that the associated linear system has at least one solution. In our case, with the info we have, we get:

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

Tonio

3. I'm sorry. I confused this issue by split 3 case: n=m, n<m,n>m . Thanks alot.