Question

Let a and b be square matrices of order 3 such that det(a) = 5 and det(b) = -2. What is the value of det(a*b)?

1) 10
2) -10
3) 7
4) -7

Answer 1

The determinant of the product of two matrices equals the product of their determinants. With det(a) = 5 and det(b) = -2, the value of det(a*b) is -10.

Step-by-step explanation:

To find the value of det(a*b), we can use the property of determinants that states the determinant of the product of two matrices is equal to the product of their determinants. Given that det(a) = 5 and det(b) = -2, we can calculate:

det(a*b) = det(a) × det(b)

det(a*b) = 5 × (-2)

det(a*b) = -10.

Therefore, the value of det(a*b) is -10.