Let A be an nxn matrix. Mark each statement True or False. Justify each answer a. The cofactor expansion of det A down a column is the negative of the cofactor expansion along a row. b. The determinant of a triangular matrix is the sum of the entries on the main diagonal. a. Choose the correct answer below. O A. True, because cofactor expansion across a row adds each of the cofactors together. Cofactor expansion down a column subtracts each cofactor from one another. This causes the two cofactor expansions to have opposite signs. OB. False, because the determinant of A can be computed by cofactor expansion across any row or down any column. Since the determinant of A is well defined, both of these cofactor expansions will be equal. OC. True, because the plus or minus sign of the (ij)-cofactor depends on the position of a; in matrix A. Cofactor expansion down a column switches the order of i andj, thereby switching the sign of the cofactor expansion across a row. OD. False, because the determinant of A can only be calculated by cofactor expansion across a row. Cofactor expansion down a column has no relation to the determinant. b. Choose the correct answer below. O A. False, because the determinant of a matrix is the arithmetic mean of the entries along the main diagonal. OB. True, because the determinant of A is the following finite series. det A= E(-1)1 +Jaydet Anj j=1 In a triangular matrix, this series simplifies to the sum of the entries along the main diagonal O C. False, because the determinant of a triangular matrix is the product of the entries along the main diagonal. OD. True, because cofactor expansion along the row (or column) with the most zeros of a triangular matrix produces a