The GATE Grind

GATE 2019 CS – Question 19

Engineering Mathematics · Linear Algebra · 1 mark · Multiple choice

Let $X$ be a square matrix. Consider the following two statements on $X$.

I. $X$ is invertible.

II. Determinant of $X$ is non-zero.

Which one of the following is TRUE?

  1. I implies II; II does not imply I.
  2. II implies I; I does not imply II.
  3. I does not imply II; II does not imply I.
  4. I and II are equivalent statements.

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Show answer and explanation

Correct answer: (D) I and II are equivalent statements.

Explanation

A square matrix is invertible exactly when its determinant is non-zero, so the two statements are equivalent.