Property

Singular matrices

A \text{ singular} \iff |A| = 0 \iff A^{-1} \text{ does not exist}

$|A|$: the determinant of A

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

questions use it

of them past-year

2018–2026

years it has appeared

11%

rated HARD

exams

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#1NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations
Strategy Concept notes
#2NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations
Strategy Concept notes
#3NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
Strategy Concept notes
#4NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
Strategy Concept notes
#5NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#6NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
Strategy Concept notes
#7NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
Strategy Concept notes
#8NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#9NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation
Strategy Concept notes
#10CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
#11CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix
#12NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation
Strategy Concept notes
#13NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation
Strategy Concept notes
#14NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations
Strategy Concept notes
#15Maharashtra HSC Class 12 → Mathematics → Matrices → Inverse by Adjoint Method
#16NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#17NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations
Strategy Concept notes
#18NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation
Strategy Concept notes
#19NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations
Strategy Concept notes
#20NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation
Strategy Concept notes
#21NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#22CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
#23CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
#24CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix
#25NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
Strategy Concept notes
#26NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
Strategy Concept notes
#27NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#28MHT-CET → Maths → Determinants and Matrices → Determinants, Cofactors and the Adjoint Identities
Strategy Concept notes

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

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