# Matrix Expression

• Jan 8th 2012, 09:21 AM
dipsy34
Matrix Expression
If A,B,X are quadratic and invertible matrices of the same size express X in terms of A ,B and their inverses. ABAXAB = A^2

I figure that if I first divide both sides with ABA I'd get XAB = (A^2) / ABA
And then it would just be to divide with AB again.

Can you do it like that? Also does matrices work like normal numbers and rules when it comes to exponents?
instead of writing A/A I an just write it like A*A^(-1)?
• Jan 8th 2012, 11:55 AM
pickslides
Re: Matrix Expression
Yes you must use the inverse rather than dividing, for example in the equation

Solving for X in \$\displaystyle AX = B\$

multiply both sides (on the left) by A inverse

\$\displaystyle A^{-1}AX = A^{-1}B\$

\$\displaystyle IX = A^{-1}B\$

\$\displaystyle X = A^{-1}B\$

This second example may also be helpful in your case as your unknown has multipliers on either side.

Solving for X in \$\displaystyle XC = D\$

multiply both sides (on the right) by C inverse

\$\displaystyle XCC^{-1} = DC^{-1}\$

\$\displaystyle XI = DC^{-1}\$

\$\displaystyle X = DC^{-1}\$

Apply this to your equation.