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Orthogonal matrix

 A square matrix with n x n elements is said to be an orthogonal matrix, if its transpose is equal to its inverse matrix.

The square matrix is also known as an orthogonal matrix when the product of a square matrix and its transpose is an identity matrix.

AT= A-1 or A.AT= I

All orthogonal matrix are square matrix but not all square matrix are orthogonal.

Orthogonal matrix is a symmetric matrix.

All identity matrix are orthogonal matrix.

The product of two orthogonal matrix is also an orthogonal matrix.

The inverse of the orthogonal matrix is also an orthogonal matrix.

The determinant of an orthogonal matrix is equal to 1 or -1

The eigenvalues of the orthogonal matrix has a value of ±1, and its eigenvectors also be an orthogonal.

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