Inverse question

1. Dec 11, 2007

eyehategod

For matrices:
is (AB)$$^{-1}$$=
A$$^{-1}$$B$$^{-1}$$
or
B$$^{-1}$$A$$^{-1}$$

Last edited: Dec 11, 2007
2. Dec 11, 2007

daveb

Are you talking about linear operators, matrices, members of a group, or what?

3. Dec 11, 2007

robphy

Since $$I=(AB)^{-1}(AB)=(AB)^{-1}AB$$
.. you can finish this off.

4. Dec 11, 2007

HallsofIvy

In other words do it! What is $(A^{-1}B^{-1})(AB)$? What is $(B^{-1}A^{-1})(AB)$?

5. Dec 11, 2007

eyehategod

so the answer is B$$^{-1}$$A$$^{-1}$$

6. Dec 11, 2007

eyehategod

what im trying to get to is this:
is there a general property.
for example:
is(BA)$$^{2}$$
equal to:
B$$^{2}$$A$$^{2}$$
or
A$$^{2}$$B$$^{2}$$

7. Dec 11, 2007

morphism

In general, no.

8. Dec 11, 2007

eyehategod

so what would the the answer for (BA)^2

9. Dec 11, 2007

morphism

(BA)^2 = BABA

So if A and B are invertible...

10. Dec 11, 2007

eyehategod

so its B^2A^2

11. Dec 11, 2007

morphism

What is B^2A^2???

12. Dec 11, 2007

rock.freak667

well normally to find a general way(an easy) way to find say A^99194

you can just represent A in the form PDP$^{-1}$ where D is the diagonalizable matrix. But I do not think you have reached that far in your course yet. If you have done eigenvalues and eigenvectors then you will understand.