Determinants

Easymathematics

If two rows of a determinant are identical, then the value of the determinant is

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Depends on the rows

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Subject: mathematics
Chapter: matrices and determinants
Topic: determinants
Difficulty: Easy
Year: 2025

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Correct Answer:

Property of Determinants:

Identical Rows: If any two rows (or columns) of a determinant are identical, its value is zero.
Reasoning: This can be proved by swapping the two identical rows. Swapping rows should negate the determinant ( $D = - D^{'}$ ). But since the rows were identical, the determinant should remain the same ( $D = D^{'}$ ). The only number satisfying $D = - D$ is $0$ .

This easy difficulty mathematics question is from the chapter matrices and determinants, covering the topic of determinants. It appeared in the 2025 exam.

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