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