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Orthogonal matrices

AAT=I  ⟺  A−1=ATAA^T = I \iff A^{-1} = A^T
ATA^T
the transpose of A

A matrix is orthogonal when its transpose is its inverse. Every rotation matrix is orthogonal, and every orthogonal matrix has determinant plus or minus one.

17
questions use it
8
of them past-year
2017–2025
years it has appeared
18%
rated HARD
2
exams
Matrices & Determinants notesOpen all 17 in the paper builder

Used alongside

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

17 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 17 of 17 questions — easiest first, then oldest paper first.

  • #1NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #2NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #3NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #4NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #5NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

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

  • #7NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #8Maharashtra HSC Class 12 → Mathematics → Matrices → Inverse by Adjoint Method

  • #9NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #10NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #11NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

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

  • #13NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #14NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

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

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

  • 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

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

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

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