Let A = (aij)nxn be a square matrix with integer entries.
a) Show that if an integer k is an eigenvalue of A, then k divides the determinant of A. n
b) Let k be an integer such that each row of A has sum k (i.e., -1 aij = k; 1 ≤ i ≤n), then [8M] show that k divides the determinant of A.