Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If det(A)=2, then det(\(A\)^T\)\(A\)^{-1}) equals:</p>
<p>(A) 1</p>
<p>(B) 2</p>
<p>(C) 4</p>
<p>(D) 1/2</p>
Step-by-Step Solution
Key Concept: det(A\)^TA^{-1}) = det(A\)^T) \times det(A\)^{-1}) = 2 \times (1/2) = 1.
1. det(\(A\)^T)=2
2. det(A\)^{-1})=1/2
3. Multiply \to 1
Correct Answer: 1