# Matrix XA=B, AY=B

1. Homework Statement

I have two 3x3 matrices A and B

and my problem is to find XA=B and AY=B

Isn't XA=B and AY=B

2. Homework Equations

3. The Attempt at a Solution

$$X=A^-^1 B$$

$$Y=A^-^1 B$$

or I am wrong?

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malawi_glenn
Homework Helper
remember that matrix multiplication is non-commutative

so yes you are wrong on the $$X=A^-^1 B$$, if XA=B

remember that matrix multiplication is non-commutative

so yes you are wrong on the $$X=A^-^1 B$$, if XA=B
Can you tell me please, what is the correct formula?

D H
Staff Emeritus
You can pre- or post-multiply a matrix equality by a matrix to yield another matrix equality: If A=B then CA = CB and AD = BD for all matrices C, D of the correct dimensionality. Use this plus the fact that matrix multiplication is associative to find a form that eliminates the matrix A from XA=B.

You can pre- or post-multiply a matrix equality by a matrix to yield another matrix equality: If A=B then CA = CB and AD = BD for all matrices C, D of the correct dimensionality. Use this plus the fact that matrix multiplication is associative to find a form that eliminates the matrix A from XA=B.
Sorry, but I don't understand what you want to say... Can you please write what equals X, and what equals Y?

$$X= ?? Y=??$$

Why don't you write out XA = AY, compare the entries and figure out what X and Y could be.

malawi_glenn
Homework Helper

You must multiply matrices from the correct order!

Take this for example:

XA=B

How would you do to eliminate X ? By multiplying inv(A) from the left?:
Then you'll get:

inv(A)XA = inv(A)B

And that is NOT you want right? So how would you do it?

You can multiply from both sides in matrix:
If you have
A=B
Then you can have
CA = CB
OR
AC = BC

The C can come in on the right or left. But you have to keep track.

So X=inv(a)B
and inv(a)AY=inv(a)B , so Y=inv(a)B

hm....

malawi_glenn
Homework Helper
Well the Y is correct, but not the X, try again

you have:

XA=B

XA=B

inv(x)XA=inv(x)B

A=inv(x)B ??

malawi_glenn
Homework Helper
well yes, but you want to solve for X right?

Read post #8, by K.J.Healey (T, 19:38)

D H
Staff Emeritus
You are supposed to be solving for X, not A. Why are you insisting on multiplying on the left? XA has two sides (left and right), and so does B.

XA=B

XA(inv (a))=B(inv (a))

X=B(inv(a))

like this?

malawi_glenn
Homework Helper
yes! Good job :-)

Thank you very much, guys. I love youuuu....

Hi all,

Pardon me for digging up this old thread, but it is related to what I am asking.
Is there some matrix manipulation that transforms equation of type xA = B into A'x' = B'? in other words, transform Unknown.KNOWN = KNOWN into KNOWN.Unknown = KNOWN.
Thanks a bunch!