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GATE 2022 AG – Question 11

Engineering Mathematics · Linear Algebra · 1 mark · Multiple choice

The determinant of a matrix remains unaltered if ______.

  1. Its columns and rows are interchanged
  2. Two parallel lines are identical
  3. Two parallel lines intersect
  4. Each element of a line is multiplied by the same factor

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Correct answer: (A) Its columns and rows are interchanged

Explanation

Transposition interchanges all rows with corresponding columns, and $\det A^T=\det A$. Thus **A**. Swapping two individual rows reverses the sign; multiplying one row by a factor multiplies the determinant by that factor. Identical rows make it zero.

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