Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=2 and \(\det(B)\)=3, then det(AB^{-1}\(A\)^{-1}) equals:</p>
Step-by-Step Solution
Key Concept: det(AB^{-1}$A$^{-1}) = $\det(A)$ \times det(B$^{-1}) \times det(A$^{-1}) = det(B$^{-1}).
1. $\det(A)$=2, det(A$^{-1})=1/2
2. Multiply: 2 \times (1/3) \times (1/2) = 1/3
Correct Answer: 1