PYQ Vault
EbooksTutor

Property

Definition of the adjoint

(adj⁡A)ij=Cji(\operatorname{adj}A)_{ij} = C_{ji}
CjiC_{ji}
the cofactor of the entry in row j, column i

The adjugate is the transpose of the matrix of cofactors. For order two this simply swaps the diagonal entries and negates the other two.

28
questions use it
18
of them past-year
2017–2025
years it has appeared
39%
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.

Filter

Filter by exam
Filter by past-year or practice

Showing 28 of 28 questions — easiest first, then oldest paper first.

  • #1NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #2Maharashtra HSC Class 12 → Mathematics → Matrices → Inverse by Adjoint Method

  • #3Maharashtra HSC Class 12 → Mathematics → Matrices → Minors, Cofactors and Adjoint

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

  • #5Maharashtra HSC Class 12 → Mathematics → Matrices → Minors, Cofactors and Adjoint

  • #6Maharashtra HSC Class 12 → Mathematics → Matrices → Inverse by Adjoint Method

  • #7Maharashtra HSC Class 12 → Mathematics → Matrices → Minors, Cofactors and Adjoint

  • #8MHT-CET → Maths → Determinants and Matrices → Determinants, Cofactors and the Adjoint Identities

  • #9NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

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

  • #11NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

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

  • #13CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix

  • #14CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix

  • #15MHT-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}.

    • #16NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #17MHT-CET → Maths → Determinants and Matrices → Determinants, Cofactors and the Adjoint Identities

  • #18NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #19NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #20NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #21NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #22NDA → 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

    • #23NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #24MHT-CET → Maths → Determinants and Matrices → Determinants, Cofactors and the Adjoint Identities

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

    • #25NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #26MHT-CET → Maths → Determinants and Matrices → Determinants, Cofactors and the Adjoint Identities

  • #27MHT-CET → Maths → Determinants and Matrices → Determinants, Cofactors and the Adjoint Identities

  • #28MHT-CET → Maths → Determinants and Matrices → Determinants, Cofactors and the Adjoint Identities

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

All Matrices & Determinants formulas