Question
What is the value of the determinant of the inverse of the matrix pmatrix -4 & -5 \\ 2 & 2 pmatrix ?
NDA
Mathematics
Matrices
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. 1 2
- B. 1
- C. 2
- D. 4
Answer
A. 1 2
Step-by-step solution
Let A = pmatrix -4 & -5 \\ 2 & 2 pmatrix . The determinant of matrix A is given by: |A| = (-4)(2) - (-5)(2) |A| = -8 + 10 = 2 The determinant of the inverse of a matrix is the reciprocal of the determinant of the matrix, i.e., |A^ -1 | = 1 |A| . |A^ -1 | = 1 2 Answer: 1 2
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