Matrices & Determinants
Inverse of a matrix
Grade 12
Question:
<p>If \(\det(A)\)=2 and \(A\) is 3 \times 3, then det(2A^{-1}) equals:</p>
<p>(A) 4</p>
<p>(B) 8/2</p>
<p>(C) 8/2? simplified</p>
<p>(D) 8/2 = 4</p>
Step-by-Step Solution
Key Concept: det(2A^{-1}) = 2^3 \times det(A$^{-1}) = 8 \times (1/2) = 4.
1. det(A$^{-1})=1/2
2. det(2A^{-1})=2^3 \times (1/2)=8/2=4
Correct Answer: 4