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Definition of the inverse

AB=BA=I  ⟺  B=A−1AB = BA = I \iff B = A^{-1}
II
the identity matrix

Two matrices are inverses precisely when their product in both orders is the identity, and the inverse when it exists is unique.

33
questions use it
16
of them past-year
2018–2026
years it has appeared
12%
rated HARD
4
exams
Matrices & Determinants notesOpen all 33 in the paper builder

Used alongside

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

33 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.

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Showing 33 of 33 questions — easiest first, then oldest paper first.

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

  • #2NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #3CBSE Class 12 → Mathematics → Matrices → Elementary Operations and Inverse of a Matrix

  • #4NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #5NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #6NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #7NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #8NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #9NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

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

  • #11NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

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

  • #13NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #14NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #15Maharashtra HSC Class 12 → Mathematics → Matrices → Inverse by Adjoint Method

  • #16NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

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

  • #18NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #19NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #20CBSE Class 12 → Mathematics → Matrices → Elementary Operations and Inverse of a Matrix

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

  • #22MHT-CET → Maths → Determinants and Matrices → Inverse of a Matrix — Adjoint Formula, Products and Verification

  • #23NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #24CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix

  • #25CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #26MHT-CET → Maths → Determinants and Matrices → Inverse of a Matrix — Adjoint Formula, Products and Verification

  • #27MHT-CET → Maths → Determinants and Matrices → Cayley–Hamilton, Matrix Polynomials and Powers

  • #28NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

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

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

  • #31NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #32MHT-CET → Maths → Determinants and Matrices → Cayley–Hamilton, Matrix Polynomials and Powers

  • #33MHT-CET → Maths → Determinants and Matrices → Cayley–Hamilton, Matrix Polynomials and Powers

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

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