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