Project ForgeEngineering Mathematics
Linear Algebra
GATE 2019
Easy
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?
- AI implies II; II does not imply I.
- BII implies I; I does not imply II.
- CI does not imply II; II does not imply I.
- I and II are equivalent statements.
Explanation
This is a fundamental theorem of linear algebra: a square matrix X is invertible if and only if det(X) ≠ 0. Neither direction is stronger than the other — they're logically equivalent conditions.
Source: GATE CS 2019 (Set-2) (2019)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.