Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=k, then det(A\)^{-1}\(A\)^nA^nA⁻^n) equals:</p>
<p>(A) 1</p>
<p>(B) k</p>
<p>(C) k^2</p>
<p>(D) k^3</p>
Step-by-Step Solution
Key Concept: Group pairs: $A$⁻^nA^n = $I$ and $A$^nA⁻^n = $I$.
1. First pair = $I$
2. Second pair = $I$
3. det(I) = 1
Correct Answer: 1