Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \det(A)=4 and \det(B)=5, then \(\det((AB)\)^{-1}) equals:</p>
<p>(A) 1/20</p>
<p>(B) 20</p>
<p>(C) 1/4</p>
<p>(D) 1/5</p>
Step-by-Step Solution
Key Concept: det((AB)^{-1}) = 1 / (det $A$ \times det $B).
1. $\det(AB)$=4 \times 5=20
2. Inverse \Rightarrow 1/20
Correct Answer: 1