Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \det(A)=2 and \det(B)=3, then \(\det(A\)\)^{-1}\(B\)^{-1}) equals:</p>
<p>(A) 1/6</p>
<p>(B) 6</p>
<p>(C) 2/3</p>
<p>(D) 3/2</p>
Step-by-Step Solution
Key Concept: det(A\)^{-1}\(B\)^{-1}) = det(A\)^{-1}) \times det(B\)^{-1}) = 1/(det \(A\) \times det \(B).
1. \(\\(\det(A)\)^{-1})=1/2, \(\det(B\)\)^{-1})=1/3
2. Multiply \to 1/6
Correct Answer: 1