In this exercise, we justify the use of elementary column operations to compute determinants. Prove that (a)

Question:

In this exercise, we justify the use of "elementary column operations" to compute determinants.
Prove that
(a) Adding a scalar multiple of one column to another does not change the determinant;
(b) Multiplying a column by a scalar multiplies the determinant by the same scalar;
(c) Interchanging two columns changes the sign of the determinant.
(d) Explain how to use elementary column operations to reduce a matrix to lower triangular form and thereby compute its determinant.
(e) Use this method to compute