### A good answer might be:

A-1Ap=A-1p
```
1  -2
0   1
```
```
1   2
0   1
```
p =
```
1  -2
0   1
```
```
5
2
```
 I p = ``` 1 -2 0 1 ``` ``` 5 2 ```
 p = ``` 1 -2 0 1 ``` ``` 5 2 ``` = ``` 1 2 ```

# Unique A-1

This is (hopefully) the same answer you got for p by trial and error a few pages ago. If A is non-singular (has an inverse) and Ap = q, then p = A-1q.

The inverse of a non-singular square matrix is unique. One way to see this is that there is only one column matrix p that is the solution to Ap = q, so there must be only one A-1.

It might look like computing A-1 is a useful thing to do. In fact, A-1 is more useful in discussions about matrices and transformations than it is in actual practice. Almost never do you really want to compute a matrix inverse.

For example, say that a column matrix p represents a point in a computer graphic world. The viewpoint changes, and the column matrix is transformed to q = Ap. If you want to talk about reversing the transformation, you talk about A-1q. But almost always there is an easier way to reverse the transformation than to compute the inverse.

### QUESTION 12:

What is   (AB) (B-1 A-1) ?