PYQ Vault
EbooksTutor

Property

Involutory matrices

A2=I  ⟺  A−1=AA^2 = I \iff A^{-1} = A
II
the identity matrix

A matrix whose square is the identity is its own inverse, and its even powers are the identity.

16
questions use it
7
of them past-year
2017–2026
years it has appeared
6%
rated HARD
3
exams
Matrices & Determinants notesOpen all 16 in the paper builder

Used alongside

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

16 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 16 of 16 questions — easiest first, then oldest paper first.

  • #1NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

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

  • #3NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

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

  • #5NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #6NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #7CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix

  • #8CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

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

  • #10CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

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

  • #12NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #13CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #14CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #15NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

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

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

All Matrices & Determinants formulas