Now that we can find the inverse, what can we do with it? As was mentioned earlier, its most apparent use is to solve the equation Ax = b. Many more uses will become apparent as you continue on your adventure into linear algebra, but several interesting facts about inverses can be found in Theorem 6, and Theorem 8 lays out some important implications if an inverse matrix exists.

As you've probably noticed, matrix inversion is closely related to other mathematical inversions you have already seen, only slightly more complicated with a few variations. We've given you the basics that you need to understand matrix inversion.

If you're interested in learning more, here are a few websites that we recommend:

• Wikipedia
• Mathworld
• Finite Mathematics