Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=4, then det(A\)⁻^3A^5A^{-1}) equals:</p>
<p>(A) 4</p>
<p>(B) 16</p>
<p>(C) 64</p>
<p>(D) 1</p>
Step-by-Step Solution
Key Concept: Exponent sum: -3 + 5 - 1 = 1 \Rightarrow $A$.
1. Expression = $A$
2. $\det(A)$ = 4
Correct Answer: 1