Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \det(A)=4, then \(\det(A\)\)^{-1}\(A\)^T) equals:</p>
<p>(A) 1</p>
<p>(B) 4</p>
<p>(C) 16</p>
<p>(D) 1/4</p>
Step-by-Step Solution
Key Concept: det(A$^{-1}$A$^T) = det(A$^{-1}) \times det(A$^T) = (1/4) \times 4 = 1.
1. $\$\det(A)$^{-1})=1/4
2. \det($A$^T)=4
3. Multiply \to 1
Correct Answer: 1