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Property

Singular matrices

A singular  ⟺  ∣A∣=0  ⟺  A−1 does not existA \text{ singular} \iff |A| = 0 \iff A^{-1} \text{ does not exist}
∣A∣|A|
the determinant of A

A square matrix fails to have an inverse exactly when its determinant is zero.

28
questions use it
13
of them past-year
2018–2026
years it has appeared
11%
rated HARD
4
exams
Matrices & Determinants notesOpen all 28 in the paper builder

Used alongside

How often each of these appears in the same solution as this one.

28 questions whose solution uses this

Every one was read individually — a question is here because its solution invokes this, not because the stem mentions it.

Every identity this chapter tests, with its own question set.

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