Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=5, then det(A\)^5A^3A⁻^7A^{-1}) equals:</p>
<p>(A) 1</p>
<p>(B) 5</p>
<p>(C) 25</p>
<p>(D) 125</p>
Step-by-Step Solution
Key Concept: Exponent sum: 5 + 3 - 7 - 1 = 0 \Rightarrow $I$.
1. Expression = $I$
2. det(I)=1
Correct Answer: 1