Determinants by cofactors

You will write three functions: one that removes a row and a column, one that finds a determinant by expanding along the first row, and one that finds the cofactor of an entry. A matrix is a list of rows. The checker tests many matrices.

The idea. The minor of the entry in row $i$ and column $j$ is the determinant that is left when row $i$ and column $j$ are deleted. A determinant is the sum, along the first row, of (entry times cofactor), and the cofactor is the minor times $(-1)^{i+j}$. A $1 \times 1$ determinant is its only entry.

Your tasks.

1. Finish submatrix(M, i, j). Return M without row i and column j.
2. Finish det(M). Expand along the first row, and call det again on the smaller matrices.
3. Finish cofactor(M, i, j). Return the sign times the determinant of submatrix(M, i, j).