Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. To find the determinant of a triangular matrix, add the entries on the main diagonal.

a. False, the determinant of a triangular matrix is equal to the order of the matrix, which may not be equal to the sum of the entries in the main diagonal.
b. False, the determinant of a triangular matrix is equal to the product of the entries in the main diagonal, which may not be equal to the sum of the entries in the main diagonal.
c. False, the determinant of a triangular matrix is equal to the number of nonzero entries in the main diagonal, which may not be equal to the sum of the entries in the main.
d. True, the determinant of a triangular matrix is equal to the order of the matrix, which is equal to the sum of the entries in the main diagonal.
e. True, the determinant of a triangular matrix is equal to the product of the entries in the main diagonal, which is equal to the sum of the entries in the main diagonal.