Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=k, then det(A\)^{-1}\(A\)^TA^{-1}\(A) equals:</p>
Step-by-Step Solution
Key Concept: Simplify: $A$^{-1}$A$ = $I$ \Rightarrow expression reduces to $A$^TA^{-1}.
1. $A$^{-1}$A$ = $I$
2. Expression becomes $A$^TA^{-1}
3. det = det(A$^T) \times det(A$^{-1})=k \times (1/k)=1
Correct Answer: 2