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