Hi,

Why is it that ifB = A^-1,

B^-1 = A

I understand that whatever you do to one side, you have to do the same for the other side, but I don't understand how (B^-1)(B^-1) = B

Can anyone please explain?

Thanks.

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- May 1st 2010, 04:10 PMCSG18Inverses
Hi,

Why is it that if**B = A^-1,**

B^-1 = A

I understand that whatever you do to one side, you have to do the same for the other side, but I don't understand how (B^-1)(B^-1) = B

Can anyone please explain?

Thanks. - May 1st 2010, 05:02 PMjakncoke
What is this in regards to? What field are we working in? Matricies?

- May 1st 2010, 09:06 PMmr fantastic
- May 2nd 2010, 04:34 AMHallsofIvy
The

**definition**of $\displaystyle X^{-1}$, in general, (matrices, elements of a group or field, etc.) is that $\displaystyle Y= X^{-1}$ if and only if $\displaystyle XY= I$**and**$\displaystyle YX= I$ where I is the "multiplicative identity" for the algebraic structure. T

If you know that $\displaystyle B= A^{-1}$ then you know that $\displaystyle AB= I$ and [mathy]BA= I[/tex], by replacing X above with A and Y with B. But if we were to replace X with B and Y with A, we wold get exactly the same equations!

Therefore, $\displaystyle A= B^{-1}$.