## anonymous 5 years ago givne a matrix A m by n.....there exist matrices C and D such that such that cA = I of n by n and AD = I m by m prove that C=D and m =n

1. anonymous

the problem is one of inverse matrices. given $AA^{-1} = A^{-1}A=I_x$ where x is the dimension of a square matrix, the rest should follow

2. anonymous

Suppose A is an m n matrix and there exist matrices C and D such that CA = In and AD = Im. Prove that m = n and C = D.

3. anonymous

$X_{mn}Y_{kl}=Z_{ml}$ and $n=m$ for any matrices X,Y Since $I_n$ is a square matrix \A_{mn}C_{xy}=I_{n} \quad n=x,\text { and }m=y=n \]

4. anonymous

$A_{mn}C_{xy}=I_{n} \quad n=x,\text { and }m=y=n$

5. anonymous

sorry, and $n=k$