Matrices & Determinants
Matrices and Determinants
star_batch_jee_advanced_2025
Grade 12
Question:
If $A$ be $3 \times 3$ non-singular matrix, $|A| = K$, then $|(xA)^{-1}| = $ (where $x \neq 0$)
xK
\frac{1}{xK}
\frac{1}{x^3 K^3}
\frac{1}{x^3 K}
Step-by-Step Solution
Key Concept: The determinant of a scaled inverse is the reciprocal of the scaled determinant.
For the inverse of a matrix, $|(xA)^{-1}| = \frac{1}{|xA|} = \frac{1}{x^n|A|} = \frac{1}{x^n K}$ where $K$ is a scalar related to $|A|$.
Correct Answer: 4