Question

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

Answer 1

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

Answer 2

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.

Answer 3

\[X_{mn}Y_{kl}=Z_{ml}\] 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 \]

Answer 4

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

Answer 5

sorry, and \[n=k\]