Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=3, then det(A\)^{-1}\(A\)^3) equals:</p>
<p>(A) 3</p>
<p>(B) 9</p>
<p>(C) 27</p>
<p>(D) 1</p>
Step-by-Step Solution
Key Concept: Simplify: $A$^{-1}$A$^3 = $A$^2.
1. $A$^{-1}$A$^3 = $A$^2
2. det(A$^2) = 3^2 = 9
Correct Answer: 2