Matrices & Determinants
Inverse of a matrix
Grade 12
Question:
<p>If \(\det(A)\)=3, then det(A\)^{-1}\(A\)^{-1}) equals:</p>
<p>(A) 1/9</p>
<p>(B) 1/3</p>
<p>(C) 3</p>
<p>(D) 9</p>
Step-by-Step Solution
Key Concept: det(A$^{-1}$A$^{-1}) = (det $A$^{-1})^2 = (1/3)^2.
1. det(A$^{-1})=1/3
2. Square \to 1/9
Correct Answer: 1