Matrices and Determinants
Adjoint of a Matrix
IIT-JEE 1999
Grade 12
Question:
If $A$ is a $3 \times 3$ matrix with $|A| = 4$, then $|\text{adj } A|$ equals:
(1) $4$
(2) $16$
(3) $64$
(4) $8$
Step-by-Step Solution
Key Concept: Recall the standard identity $|\text{adj } A| = |A|^{n-1}$ for an $n \times n$ matrix $A$, and substitute $n = 3$ along with the given value of $|A|$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)