In advanced linear algebra, one proves the following determinant criterion for rank: The rank of a matrix A is r if and only if A has some r × r submatrix with a nonzero determinant, and all square submatrices of larger size have determinant zero. (A submatrix of A is any matrix obtained by deleting rows or columns of A. The matrix A itself is also considered to be a submatrix of A.) In each part, use this criterion to find the rank of the matrix.
(a)

(b)

(c)

(d)

1 0 2 41 2 1 2 3 2 4 6 0 123 1 1 2 0 3 -1 2 40