Which of the following best defines a singular matrix?

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Multiple Choice

Which of the following best defines a singular matrix?

A singular matrix is a square matrix that does not have an inverse. This happens exactly when its determinant is zero, which means the rows or columns are linearly dependent. So the option that says it does not have an inverse is the definitive statement. If a matrix did have an inverse, it would be non-singular, which corresponds to a nonzero determinant. Saying the determinant is nonzero describes the opposite situation. Saying the matrix has identical rows shows a specific way to be singular, but the general definition is about invertibility, not just a particular case.

A singular matrix is a square matrix that does not have an inverse. This happens exactly when its determinant is zero, which means the rows or columns are linearly dependent. So the option that says it does not have an inverse is the definitive statement.

If a matrix did have an inverse, it would be non-singular, which corresponds to a nonzero determinant. Saying the determinant is nonzero describes the opposite situation. Saying the matrix has identical rows shows a specific way to be singular, but the general definition is about invertibility, not just a particular case.

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