Question
If M is a square matrix such that M^3=M, then how many values of |M| are possible ?
NDA
Mathematics
Matrices
2026
NDA 2026 (Phase 1)
NDA Mathematics Question (2026) — Solution
Options
- A. One
- B. Two
- C. Three
- D. Four
Answer
C. Three
Step-by-step solution
Given M^3 = M Taking determinant on both sides, we get: |M^3| = |M| Using the property |A^n| = |A|^n, we have: |M|^3 = |M| |M|^3 - |M| = 0 |M|(|M|^2 - 1) = 0 |M|(|M| - 1)(|M| + 1) = 0 |M| = 0, 1, -1 Thus, there are three possible values for |M|. Answer: Three
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