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The adjoint identity

A(adj⁡A)=(adj⁡A)A=∣A∣ InA(\operatorname{adj}A) = (\operatorname{adj}A)A = |A|\,I_n
AA
a square matrix
∣A∣|A|
the determinant of A
adj⁡A\operatorname{adj}A
the adjugate — transpose of the cofactor matrix
InI_n
the identity matrix of order n

A matrix times its adjugate, in either order, is the determinant times the identity matrix.

34
questions use it
20
of them past-year
2018–2026
years it has appeared
15%
rated HARD
4
exams
Matrices & Determinants notesOpen all 34 in the paper builder

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34 questions whose solution uses this

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Showing 34 of 34 questions — easiest first, then oldest paper first.

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

  • #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 → Minors, Cofactors and Adjoint

  • #6NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #7MHT-CET → Maths → Determinants and Matrices → Determinants, Cofactors and the Adjoint Identities

  • #8CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix

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

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

  • #11Maharashtra HSC Class 12 → Mathematics → Matrices → Minors, Cofactors and Adjoint

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

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

  • #14Maharashtra HSC Class 12 → Mathematics → Matrices → Minors, Cofactors and Adjoint

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

  • #16NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #17NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #18Maharashtra HSC Class 12 → Mathematics → Matrices → Minors, Cofactors and Adjoint

  • #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

  • #23CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix

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

    • #24NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #25CBSE Class 12 → Mathematics → Determinants → Solving System of Linear Equations

  • #26CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix

  • #27NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #28CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix

  • #29CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix

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

  • #31MHT-CET → Maths → Determinants and Matrices → Determinants, Cofactors and the Adjoint Identities

  • #32MHT-CET → Maths → Determinants and Matrices → Determinants, Cofactors and the Adjoint Identities

  • #33MHT-CET → Maths → Determinants and Matrices → Determinants, Cofactors and the Adjoint Identities

  • #34MHT-CET → Maths → Determinants and Matrices → Determinants, Cofactors and the Adjoint Identities

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

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