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📐 Mathematics  ·  Matrices  ·  JEE

If a square matrix A satisfies A² = 0, then (I − A)⁻¹ equals:

Answer: I + A.

  • A I − A
  • B I + A
  • C I
  • D A

Correct answer: B. I + A

Explanation: (I − A)(I + A) = I − A² = I, so (I − A)⁻¹ = I + A.

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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