Inverse by the adjoint

You will build the inverse of a square matrix from cofactors. The functions submatrix and det are already written. A matrix is a list of rows. The checker tests many matrices.

The idea. The cofactor of the entry in row $i$ and column $j$ is $(-1)^{i+j}$ times the determinant of the matrix with that row and column deleted. The adjoint is the transpose of the cofactor matrix. The inverse is the adjoint divided by the determinant, and it does not exist when the determinant is $0$.

Your tasks.

1. Finish cofactor_matrix(M). Return the matrix of all the cofactors.
2. Finish adjoint(M). Return the transpose of the cofactor matrix.
3. Finish inverse(M). Return the inverse as a list of rows, or None if the determinant is 0.