C) The determinant of 2 x 2 matrix A is 3. If you switch the rows and multiply the first row by 6 and the second row by 2, explain how to find determinant and provide the answer

Step-by-step explanation:

A 2 * 2 matrix has 2 rows and 2 columns

Let us assume that matrix A is expressed as

a b

c d

The determinant of matrix A would be

(a * d) - (b * c)

Given that the determinant of matrix A is 3, it means that

ad + bc = 3

If we switch the rows, the first row becomes cd and the second row becomes ab. If we multiply the first row by 6 and the second row by 2, the matrix becomes

6c 6d

2a 2b

The determinant would be

(6c * 2b) - (2a * 6d)

Determinant = 12bc - 12ad