One helpful intuition not explicitly stated: To rotate a 2x2 matrix by 90°, you can multiply it by: ┌ ┐ │ 0 -1 │ │ 1 0 │ └ ┘

One helpful intuition not explicitly stated: To rotate a 2x2 matrix by 90°, you can multiply it by: ┌ ┐ │ 0 -1 │ │ 1 0 │ └ ┘ One could reason out how to expand this into 3 dimensions. For example: ┌ ┐ x: │ 0 -1 0 │ y: │ 1 0 0 │ z: │ 0 0 1 │ └ ┘ performs the rotation along the x and y axes. One could verify that the 2x2 example above is equivalent to: ┌ ┐ ┌ ┐ │ 0 -1 │ = │ cos(θ) -sin(θ) │ │ 1 0 │ │ sin(θ) cos(θ) │ └ ┘ └ ┘ when θ is 90°, and that this formula works for any angle, and the 3D example expands similarly. When imagining how I want something to rotate, I occasionally find it helpful to start at the first matrix and reason outward from there.