How many invertible $ 3 \times 3 $ matrices exist over $2$-element field?
Obviously if some field has only $2$ elements, those elements must be $0$ and $1$. A matrix is invertible if and only if its determinant is non zero. I think it will be easier to find matrices which determinants are $0$ and subtract that number from $2^9$ (total number of matrices we can build over that field).
Is there any "clever" way of solving this problem?