Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \det(A) = 4, then \(\det(A\)\)^{-1}\(B) where \det(B)=2 is:</p>
<p>(A) 1/2</p>
<p>(B) 1/8</p>
<p>(C) 2</p>
<p>(D) 8</p>
Step-by-Step Solution
Key Concept: det(A\)^{-1}\(B) = det(A\)^{-1}) \times \(\det(B)\) = (1/det \(A) \times \(\det(B)\).
1. \(\\(\det(A)\)^{-1})=1/4
2. Multiply with \det(B)=2
3. = 2/4 = 1/2
Correct Answer: 1