Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=5, then det(A\)⁻^2A^4A^{-1}) equals:</p>
<p>(A) 5</p>
<p>(B) 25</p>
<p>(C) 125</p>
<p>(D) 1</p>
Step-by-Step Solution
Key Concept: Simplify: $A$⁻^2A^4A^{-1} = $A$.
1. Total exponent = 1
2. Expression = $A$
3. $\det(A)$=5
Correct Answer: 1