Simple rules for a simple 2 players game:
1- Choose the size of your matrix.
2- Choose the defender and the attacker, the defender must prevent the matrix from becoming invertible, the attacker must make it invertible.
3- Each in turn, add a 0 or a 1 (the matrix takes its values in Z/2Z) somewhere in the matrix.
4- The defender wins if the matrix is not invertible, otherwise the attacker wins.
5- Good luck!
This game has been created by AG and his friends in the ENS of Cachan in the early 2000's.