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Property

Orthogonal matrices

AAT=I    A1=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.

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

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