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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.

Correct answer: I and II are equivalent statements.

Solution

A square matrix is invertible if and only if its determinant is non-zero, meaning that both statements are true simultaneously or false simultaneously. Therefore, I and II are equivalent statements.

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