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Questions › GATE › GATE 2026 › Q27
1 mark, −0.333Mathematics › Matrices, determinants and linear systems › Singular matrices and invertibilityModerateabout 1 min

GATE 2026 Question 27: Matrices, determinants and linear systems

AAA is an (n×n)(n \times n)(n×n) matrix. Consider the following two statements

Statement 1: Columns of matrix AAA are linearly independent

Statement 2: Inverse of matrix AAA exists

Which one of the following statements is TRUE?

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Plain-text version

A is an (n × n) matrix. Consider the following two statements Statement 1: Columns of matrix A are linearly independent Statement 2: Inverse of matrix A exists Which one of the following statements is TRUE? (A) Statement 1 is true if and only if Statement 2 is true (B) Statement 1 and Statement 2 can be individually true or false (C) Statement 1 implies Statement 2 but not the other way round (D) Statement 2 implies Statement 1 but not the other way round

Also written as: A is an (n * n) matrix. Consider the following two statements Statement 1: Columns of matrix A are linearly independent Statement 2: Inverse of matrix A exists Which one of the following statements is TRUE?

Matrices, determinants and linear systems has come up 102 times in 7 exams since 2006.

What this question tests

This question is on Singular matrices and invertibility, part of Matrices, determinants and linear systems in Mathematics.

When a matrix has an inverse and what singularity means.

TestStop has 17 past-paper questions on this subtopic.

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Question from the GATE 2026 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.