Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=k, then det(A\)^nA^{-m}) where n=m equals:</p>
<p>(A) 1</p>
<p>(B) k</p>
<p>(C) k^2</p>
<p>(D) 0</p>
Step-by-Step Solution
Key Concept: If n=m \Rightarrow $A$^nA⁻^n = $I$.
1. n=m \Rightarrow exponent = 0
2. Matrix = $I$
3. det(I) = 1
Correct Answer: 1