Question
For the following two (02) items: Let A = pmatrix & \\ - & pmatrix . What is the value of the determinant of the matrix A^4?
NDA
Mathematics
Matrices
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. 0
- B. 1
- C. 4 - 4
- D. ^2 4 - ^2 4
Answer
B. 1
Step-by-step solution
The determinant of matrix A is given by: |A| = ( ) - (- ) |A| = ^2 + ^2 = 1 Using the property of determinants |A^n| = |A|^n, we have: |A^4| = |A|^4 = 1^4 = 1 Answer: 1
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