Explore orthogonal matrices and their properties in this 17-minute linear algebra video. Delve into the definition of orthogonal matrices, examine examples like standard rotation and reflection matrices, and prove a crucial theorem establishing the equivalence between orthogonality and having orthonormal row and column vectors. Learn about basic properties of orthogonal matrices and understand the geometry of orthogonal transformations. Gain insights into this important concept through clear explanations and practical examples, enhancing your understanding of linear algebra fundamentals.