Inverses: B is inverse of A; find X so XA = C for C =....

[mental]

Does anyone know how to solve for:
Matrix A has inverese

B= [ 2 1 3 ]
     1 1 1
     4 2 1

I need to find a matrix X such that XA=C, where

C= [ 1 2 3 ]
     1 0 1
     0 0 0

Any ideas will be helpful. Thanks

[stapel_eliz]

Matrix A has inverese

B= [ 2 1 3 ]
     1 1 1
     4 2 1

I need to find a matrix X such that XA=C, where

C= [ 1 2 3 ]
     1 0 1
     0 0 0

You are given that AB = BA = I, the identity matrix. You are given B and C. You are asked to solve "XA = C" for X.

To solve using inverses, multiply each side of the equation, "on the right", by the inverse of A:

. . . . .(XA)A^-1 = (C)A^-1

This leaves you with X(AA^-1) = X(I) = X = CA^-1 = CB.

Multiply it out to find X.

[mental]

Thanks a lot! I actually managed to solve for Y but couldn't rationalize enough to get X. It's greatly appreciated!!!