An orthogonal matrix is a square matrix whose rows and columns are orthonormal vectors. This means that the dot product of any two different rows or columns is zero, while the dot product of a row or column with itself is one. Mathematically, a matrix A is orthogonal if A^T A = I , where A^T is the transpose of A and I is the identity matrix. Orthogonal matrices have several important properties. They preserve the length of vectors when multiplied, which makes them useful in computer graphics and signal processing. Additionally, the inverse of an orthogonal matrix is simply its transpose, simplifying calculations in various applications, including machine learning and numerical analysis.