Matrices and Determinants
Inverse of a Matrix
JEE Main 2019
Grade 12
Question:
If $A$ is a $3 \times 3$ invertible matrix with $|A| = 5$, then $|A^{-1}|$ equals:
(1) $5$
(2) $25$
(3) $\frac{1}{5}$
(4) $\frac{1}{25}$
Step-by-Step Solution
Key Concept: Start from $AA^{-1} = I$, take determinants of both sides using $|XY| = |X||Y|$, and recall that $|I| = 1$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)