Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=k, then det(A\)^nA⁻^n) equals:</p>
<p>(A) 1</p>
<p>(B) k</p>
<p>(C) k^2</p>
<p>(D) depends</p>
Step-by-Step Solution
Key Concept: $A$^nA⁻^n = $I$ for any integer n.
1. $A$^nA⁻^n = $I$
2. det(I) = 1
Correct Answer: 1