Check whether a square matrix satisfies A·Aᵀ = the identity matrix.
How It Works
How Orthogonal Matrix Checker Works
The calculator multiplies the matrix by its transpose and checks whether the result is the identity matrix — when it is, the matrix's transpose is also its inverse, and the matrix represents a pure rotation or reflection that preserves length and angles.
Worked Example
See It In Action
A 90° rotation matrix, rows 0,-1 / 1,0, is orthogonal — rotating never stretches or distorts the space.
FAQ
Frequently Asked Questions
Why are orthogonal matrices useful?
Because they preserve distances and angles, they're the natural way to represent rotations and reflections in computer graphics, robotics, and physics without introducing any scaling distortion.
Does an orthogonal matrix always have determinant ±1?
Yes — a determinant of +1 corresponds to a pure rotation, while −1 corresponds to a reflection (or a rotation combined with a reflection).
