Orthogonal matrix   - properties and formulas -

Table of contents
- Definition
- Example
  Let $R$ be a square matrix. $R$ is called orthtonal matrix if it satisfies
Definition of orthogonal matrix
, where $R^T$ denotes the transpose of $R$, and $I$ denotes the identity matrix.
  Show that the following matrix
An example of orthogonal matrix
is an orthogonal matrix.
  By calculating concretely, we have
An example of orthogonal matrix
Therefore, $R$ is an orthogonal matrix.