PYQ Vault
EbooksTutor

Formula

Inverse via the adjoint

A−1=1∣A∣adj⁡A(∣A∣≠0)A^{-1} = \frac{1}{|A|}\operatorname{adj}A \qquad (|A| \neq 0)
AA
a square matrix
∣A∣|A|
the determinant of A
adj⁡A\operatorname{adj}A
the adjugate — transpose of the cofactor matrix

The inverse of a non-singular matrix is its adjugate divided by its determinant.

41
questions use it
29
of them past-year
2017–2026
years it has appeared
29%
rated HARD
4
exams
Matrices & Determinants notesOpen all 41 in the paper builder

Used alongside

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

41 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.

Filter

Filter by exam
Filter by past-year or practice

Showing 41 of 41 questions — easiest first, then oldest paper first.

  • #1Maharashtra HSC Class 12 → Mathematics → Matrices → Inverse by Adjoint Method

  • #2NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #3NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #4NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #5Maharashtra HSC Class 12 → Mathematics → Matrices → Inverse by Adjoint Method

  • #6MHT-CET → Maths → Determinants and Matrices → Inverse of a Matrix — Adjoint Formula, Products and Verification

  • #7MHT-CET → Maths → Determinants and Matrices → Inverse of a Matrix — Adjoint Formula, Products and Verification

  • #8MHT-CET → Maths → Determinants and Matrices → Inverse of a Matrix — Adjoint Formula, Products and Verification

  • #9MHT-CET → Maths → Determinants and Matrices → Determinants, Cofactors and the Adjoint Identities

  • #10NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #11Maharashtra HSC Class 12 → Mathematics → Matrices → Inverse by Adjoint Method

  • #12NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #13NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #14NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #15NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #16MHT-CET → Maths → Determinants and Matrices → Inverse of a Matrix — Adjoint Formula, Products and Verification

  • #17MHT-CET → Maths → Determinants and Matrices → Cayley–Hamilton, Matrix Polynomials and Powers

  • #18MHT-CET → Maths → Determinants and Matrices → Cayley–Hamilton, Matrix Polynomials and Powers

  • #19NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #20MHT-CET → Maths → Determinants and Matrices → Inverse of a Matrix — Adjoint Formula, Products and Verification

  • #21CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix

  • #22CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix

  • #23MHT-CET → Maths → Determinants and Matrices → Inverse of a Matrix — Adjoint Formula, Products and Verification

  • #24MHT-CET → Maths → Determinants and Matrices → Cayley–Hamilton, Matrix Polynomials and Powers

  • #25MHT-CET → Maths → Determinants and Matrices → Inverse of a Matrix — Adjoint Formula, Products and Verification

  • Set · 1 question
    For the following two (02) items: Let A=(cos⁡θsin⁡θ−sin⁡θcos⁡θ)A=\begin{pmatrix}\cos\theta & \sin\theta\\-\sin\theta & \cos\theta\end{pmatrix}.

    • #26NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #27CBSE Class 12 → Mathematics → Determinants → Solving System of Linear Equations

  • #28MHT-CET → Maths → Determinants and Matrices → Inverse of a Matrix — Adjoint Formula, Products and Verification

  • #29NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #30NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #31Maharashtra HSC Class 12 → Mathematics → Matrices → Inverse by Adjoint Method

  • #32NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • Set · 1 question
    Consider the following for the next three (03) items that follow: If A=(1000cos⁡θsin⁡θ0sin⁡θ−cos⁡θ)A = \begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos\theta & \sin\theta \\ 0 & \sin\theta & -\cos\theta \end{pmatrix}, which of the following are correct? 1. A+adjAA + adjA is a null matrix 2. A−1+adjAA^{-1} + adjA is a null matrix 3. A−A−1A - A^{-1} is a null matrix

    • #33NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #34MHT-CET → Maths → Determinants and Matrices → Inverse of a Matrix — Adjoint Formula, Products and Verification

  • #35MHT-CET → Maths → Determinants and Matrices → Cayley–Hamilton, Matrix Polynomials and Powers

  • #36MHT-CET → Maths → Determinants and Matrices → Inverse of a Matrix — Adjoint Formula, Products and Verification

  • #37MHT-CET → Maths → Determinants and Matrices → Cayley–Hamilton, Matrix Polynomials and Powers

  • Set · 1 question
    Let A=(3−342−340−11)A=\begin{pmatrix}3&-3&4\\2&-3&4\\0&-1&1\end{pmatrix}.

    • #38NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #39MHT-CET → Maths → Determinants and Matrices → Inverse of a Matrix — Adjoint Formula, Products and Verification

  • #40MHT-CET → Maths → Determinants and Matrices → Inverse of a Matrix — Adjoint Formula, Products and Verification

  • #41MHT-CET → Maths → Determinants and Matrices → Inverse of a Matrix — Adjoint Formula, Products and Verification

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

All Matrices & Determinants formulas