Consider the 2 × 2 matricesand where x and y denote the row vectors of B. Then the product...

Consider the 2 × 2 matrices

and

where x and y denote the row vectors of B. Then the product AB can be written in the form

Use this expression and the properties of determinants to show that

Thus the determinant of a product of 2 × 2 matrices is equal to the product of their determinants.