Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=k, then det(A\)^nA^mA⁻^m) equals:</p>
<p>(A) k^n</p>
<p>(B) k^m</p>
<p>(C) k</p>
<p>(D) 1</p>
Step-by-Step Solution
Key Concept: Cancel $A$^m and $A$⁻^m \Rightarrow remaining $A$^n.
1. $A$^mA⁻^m = $I$
2. Expression = $A$^n
3. det = k^n
Correct Answer: 1