Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=k, then det(A\)^{-1}\(A\)^2A^{-1}) equals:</p>
<p>(A) k</p>
<p>(B) 1</p>
<p>(C) k^2</p>
<p>(D) 1/k</p>
Step-by-Step Solution
Key Concept: Simplify first: $A$^{-1}$A$^2A^{-1} = $I$.
1. $A$^{-1}$A$^2 = $A$
2. $A$ \cdot $A$^{-1} = $I$
3. det(I)=1
Correct Answer: 2