Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=3, then det((A\)^4A⁻^4)^5) equals:</p>
<p>(A) 1</p>
<p>(B) 3</p>
<p>(C) 9</p>
<p>(D) 243</p>
Step-by-Step Solution
Key Concept: Inside simplifies to identity, so result remains 1.
1. $A$^4A⁻^4 = $I$
2. $I$^5 = $I$
3. det(I)=1
Correct Answer: 1