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📐 Mathematics  ·  Matrices  ·  JEE

If a square matrix A satisfies A² = A and A ≠ I, then det(A) equals:

Answer: 0.

  • A 1
  • B 0
  • C −1
  • D 2

Correct answer: B. 0

Explanation: A² = A gives det(A)² = det(A), so det(A) is 0 or 1; since A ≠ I and A is singular here, det(A) = 0.

Matrix A (3 rows x 3 columns)a11a12a13a21a22a23a31a32a33column 1column 2column 3row 1row 2row 3

Element aij of matrix A sits at the intersection of row i and column j.

Concept context

Matrix operations, determinants, inverses, and solving linear systems

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