In AES the forward affine tranformation matrix is defined as:

| 1 0 0 0 1 1 1 1 |
| 1 1 0 0 0 1 1 1 |
| 1 1 1 0 0 0 1 1 |
| 1 1 1 1 0 0 0 1 |
| 1 1 1 1 1 0 0 0 |
| 0 1 1 1 1 1 0 0 |
| 0 0 1 1 1 1 1 0 |
| 0 0 0 1 1 1 1 1 |

and the inverse affine transformation matrix is defined as:

| 0 0 1 0 0 1 0 1 |
| 1 0 0 1 0 0 1 0 |
| 0 1 0 0 1 0 0 1 |
| 1 0 1 0 0 1 0 0 |
| 0 1 0 1 0 0 1 0 |
| 0 0 1 0 1 0 0 1 |
| 1 0 0 1 0 1 0 0 |
| 0 1 0 0 1 0 1 0 |

How is the inverse affine transformation derived from the forward affine transformation?

In AES the forward affine tranformation matrix is defined as:

$$ \begin{bmatrix} 1& 0& 0& 0& 1& 1& 1& 1 \\ 1& 1& 0& 0& 0& 1& 1& 1 \\ 1& 1& 1& 0& 0& 0& 1& 1 \\ 1& 1& 1& 1& 0& 0& 0& 1 \\ 1& 1& 1& 1& 1& 0& 0& 0 \\ 0& 1& 1& 1& 1& 1& 0& 0 \\ 0& 0& 1& 1& 1& 1& 1& 0 \\ 0& 0& 0& 1& 1& 1& 1& 1 \\ \end{bmatrix}$$

and the inverse affine transformation matrix is defined as:

$$ \begin{bmatrix} 0& 0& 1& 0& 0& 1& 0& 1 \\ 1& 0& 0& 1& 0& 0& 1& 0 \\ 0& 1& 0& 0& 1& 0& 0& 1 \\ 1& 0& 1& 0& 0& 1& 0& 0 \\ 0& 1& 0& 1& 0& 0& 1& 0 \\ 0& 0& 1& 0& 1& 0& 0& 1 \\ 1& 0& 0& 1& 0& 1& 0& 0 \\ 0& 1& 0& 0& 1& 0& 1& 0 \\ \end{bmatrix}$$

How is the inverse affine transformation derived from the forward affine transformation?