Product of determinants

Let  and  be two determinants. Then, the product Δ₁Δ₂ is defined as 

This is row-by-column multiplication value for finding the product of two determinants and it is same as the rule of multiplication of two matrices. Since the value of a determinant does not alter by interchanging the rows and columns. So, we can also follow the row-by-row or the column –by-row or column-by-column multiplication rule.

Ex:

If . Show that 

Sol:

We have,