Matrices and Determinants
Adjoint of a Matrix
JEE Main 2020
Grade 12
Question:
If $A$ is a $3 \times 3$ matrix with $|A| = 2$, then $|\text{adj } A|$ equals:
(1) $4$
(2) $2$
(3) $8$
(4) $1$
Step-by-Step Solution
Key Concept: Apply the identity $|\text{adj } A| = |A|^{n-1}$ for a square matrix of order $n$, taking $n = 3$ here.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)