Question
For the following two (02) items: Let A = pmatrix & \\ - & pmatrix . What is [ adj \, A]^ -1 equal to?
NDA
Mathematics
Matrices
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. -A
- B. -A^T
- C. A
- D. A^T
Answer
C. A
Step-by-step solution
Given A = pmatrix & \\ - & pmatrix The determinant of A is |A| = ^2 - (- )( ) = ^2 + ^2 = 1 For any non-singular matrix, the inverse is given by A^ -1 = 1 |A| adj \, A Substituting |A| = 1, we get adj \, A = A^ -1 Taking the inverse on both sides yields [ adj \, A]^ -1 = (A^ -1 )^ -1 = A Answer: A
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