Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \det(A) = 2 and \det(B) = 3, then \(\det(A\)\)^{-1}\(B\)^2) is:</p>
<p>(A) 9/2</p>
<p>(B) 3/2</p>
<p>(C) 6</p>
<p>(D) 18</p>
Step-by-Step Solution
Key Concept: det(A$^{-1}$B$^2) = det(A$^{-1}) \times (det $B)^2.
1. $\$\det(A)$^{-1})=1/2
2. \det($B$^2)=3^2=9
3. Multiply \to 9/2
Correct Answer: 1