Let A, B and C be n n matrices such that det(A) = 4, det(B) = 3 and det(C) = -1

(a) Find the determinant of 2AB^-1

(b) Find the determinant of A after the following operations in order:

• i Multiply row i by 3;
• ii Multiply row j by 2;
• iii Add row i to row j;
• iv Add k times row j to row i

(c) Suppose B and C match on all but row j. Find the determinant of the matrix that has the same rows of B and C for i j and the sum of 3 times row j from B and 4 times row j from C for i = j