How can I solve for a matrix when given its inverse?

Question

The inverse of a matrix A is given by:
| 3 4 |
| 5 6 |

How can I solve for A?

Answer 1

Find the inverse of the given matrix. The inverse of the inverse of a matrix is the original matrix.
In case you don't know how to find the inverse of a matrix:
| 3 4 | _ |1 2 | |1 2 | |1 2 | |1 0 |
| 5 6 | _ | 5 6 | |0 4 | | 0 1 | | 0 1 |
| 1 0 | | 2 -1| |2 - 1 | |2 - 1 | | -3 2 |
| 0 1 | | 0 1| | 10 -6| | 5/2 -3/2| |5/2 -3/2|
The inverse matrix is given at the end of the last two lines.
Congratulations, this is the only matrix I've ever done online and the only one I'm ever going to do. It's a pain.
In any case if you have any questions: [e-mail]

Answer 2

Invert the inverse to get A:
The inverse of A is
-1/2 * | 6 -4|
..........| -5 3|
and that's A.