Question
If f( ) = pmatrix & \\ - & pmatrix , then what is \ f( )\ ^2 equal to?
NDA
Mathematics
Matrices
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. pmatrix -1 & 0 \\ 0 & -1 pmatrix
- B. pmatrix 1 & 1 \\ 1 & 1 pmatrix
- C. pmatrix -1 & 0 \\ 0 & 1 pmatrix
- D. pmatrix 1 & 0 \\ 0 & 1 pmatrix
Answer
D. pmatrix 1 & 0 \\ 0 & 1 pmatrix
Step-by-step solution
Given f( ) = pmatrix & \\ - & pmatrix Substituting = : f( ) = pmatrix & \\ - & pmatrix = pmatrix -1 & 0 \\ 0 & -1 pmatrix Squaring the matrix: \ f( )\ ^2 = pmatrix -1 & 0 \\ 0 & -1 pmatrix pmatrix -1 & 0 \\ 0 & -1 pmatrix = pmatrix 1 & 0 \\ 0 & 1 pmatrix
Related: Mathematics — Matrices · All PYQ Banks