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4x4 matrix [R|t] is the mixture of 3x3 rotation matrix R and translation 3D vector t. Let's call [R|t] transformation matrix.

- Lemma
- Multiplying rotation matrix and rotation matrix results in rotation matrix
- Lemma
- Multiplying transformation matrix and transformation matrix results in transformation matrix
- Lemma
- The inverse of rotation matrix is its transpose
- Lemma
- The inverse of transformation matrix always exists
- Proof
- It is apparant from the definition of rotation matrix and transformation matrix

The inverse of transformation matrix [R|t] is [R^T | - R^T t].