Product of Determinants

Rule for multiplication of two determinants is the same as the rule for multiplication of two matrices.

While multiplying two matrices row-by-column rule alone can be followed. The process of interchanging the rows and columns will not affect the value of the determinant. Therefore, you can adopt the following procedures for multiplication of two determinants:

• Row-by-row multiplication rule
• Column-by-column multiplication rule
• Column-by-row multiplication rule

The determinant of the product matrix is equal to the product of the individual determinant values of the square matrices of same order.

Let A and B be two square matrices of the same order.

|AB| = |A| |B|