Thread: Inverses

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.

What is this in regards to? What field are we working in? Matricies?

Originally Posted by CSG18

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.

.

Alternatively, note that . But if then

The definition of , in general, (matrices, elements of a group or field, etc.) is that if and only if and where I is the "multiplicative identity" for the algebraic structure. T

If you know that then you know that 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, .