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NDA 2026
Exam
NDA
Year
2026
Subject
Mathematics
Chapter
Matrices

NDA 2026 · Mathematics · Matrices

If M is a square matrix such that M^3=M , then how many values of...

If MM is a square matrix such that M3=MM^3=M, then how many values of ∣M∣|M| are possible ?

Options

  1. AOne
  2. BTwo
  3. CThree
  4. DFour

Correct answer

C. Three

Step-by-step solution

Given M3=MM^3 = M

Taking determinant on both sides, we get:

∣M3∣=∣M∣|M^3| = |M|

Using the property ∣An∣=∣A∣n|A^n| = |A|^n, we have:

∣M∣3=∣M∣|M|^3 = |M|

∣M∣3−∣M∣=0|M|^3 - |M| = 0

∣M∣(∣M∣2−1)=0|M|(|M|^2 - 1) = 0

∣M∣(∣M∣−1)(∣M∣+1)=0|M|(|M| - 1)(|M| + 1) = 0

∣M∣=0,1,−1|M| = 0, 1, -1

Thus, there are three possible values for ∣M∣|M|.

Answer: Three
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