## Time for action – inverting matrices

The inverse of a matrix `A` in linear algebra is the matrix `A-1`, which, when multiplied with the original matrix, is equal to the identity matrix `I`. This can be written as follows:

`A A-1 = I`

The `inv()` function in the `numpy.linalg` package can invert an example matrix with the following steps:

1. Create the example matrix with the `mat()` function we used in the previous chapters:

```A = np.mat("0 1 2;1 0 3;4 -3 8")
print("A\n", A)```

The `A` matrix appears as follows:

```A
[[ 0  1  2]
[ 1  0  3]
[ 4 -3  8]]
```
2. Invert the matrix with the `inv()` function:

```inverse = np.linalg.inv(A)
print("inverse of A\n", inverse)```

The inverse matrix appears as follows:

```inverse of A
[[-4.5  7.  -1.5]
[-2.   4.  -1. ]
[ 1.5 -2.   0.5]]
```

### Tip

If the matrix is singular, or not square, a `LinAlgError` is raised. If you want, you can check the result manually with a pen and paper. This is left as an exercise for the reader.

3. Check the result by multiplying the original matrix with the result of the `inv()` function...