The game begins with an invertible matrix of non-negative integers. Each turn ends with a player reducing one of the entries of the matrix, so that it is still a non-negative integer. If the resulting matrix is non-invertible, that is a losing move. Depending on how cutthroat you want to play, it might be up to the other player to notice you created a non-invertible matrix at the beginning of their turn.
I've played with my matrix algorithms class a few time|s this semester, using this as the starting position:
| 1 2 |
| 3 4 |
This position is in Fuzzy. What's the winning move?