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📐 Mathematics  ·  Matrices  ·  JEE

A square matrix A is invertible if and only if:

Answer: |A| ≠ 0.

  • A |A| ≠ 0
  • B |A| = 0
  • C A = I
  • D A is symmetric

Correct answer: A. |A| ≠ 0

Explanation: A matrix has an inverse precisely when its determinant is non-zero (non-singular).

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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