If A and B given, then what is determinant of AB

• Matrices Determinants

If \( A = \begin{bmatrix}1 & 2 \\2 & 3 \end{bmatrix} \) and \( B = \begin{bmatrix}1 & 0 \\1 & 0 \end{bmatrix} \) then what is determinant of AB?

1. 0
2. 1
3. 10
4. 20

Solution

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

|AB| = |A| |B|

Since determinant of B = 0, |AB| = 0

The correct option is A.