Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=k, then det(A\)⁻^nA^m) where m>n equals:</p>
<p>(A) k^(m-n)</p>
<p>(B) k^(n-m)</p>
<p>(C) 1</p>
<p>(D) k</p>
Step-by-Step Solution
Key Concept: Combine powers: $A$^(m-n), then apply determinant power rule.
1. $A$^{-1}$A$^m = $A$^(m-n)
2. det = k^(m-n)
Correct Answer: 1