Matrices & Determinants
Inverse of a matrix
Grade 12
Question:
<p>If \(\det(A)\)=2, then det((A\)^{-1})^T) equals:</p>
<p>(A) 1/2</p>
<p>(B) 2</p>
<p>(C) 1</p>
<p>(D) 4</p>
Step-by-Step Solution
Key Concept: Transpose does not change determinant; inverse gives reciprocal.
1. det(A$^{-1})=1/2
2. Transpose \Rightarrow same
3. Answer = 1/2
Correct Answer: 1