Zaymiey

📐 Mathematics  ·  Matrices  ·  JEE

If A is a 3×3 orthogonal matrix, then det(A) equals:

Answer: ±1.

  • A 0
  • B 1
  • C ±1
  • D 3

Correct answer: C. ±1

Explanation: AAᵀ = I gives det(A)² = 1, so det(A) = ±1.

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

Read the full Matrices notes →