How to verify that a matrix is orthogonal?

How to verify that a matrix is orthogonal?

There are two methods
1. Use definition
If AA ^ t is equal to the identity matrix e, it is an orthogonal matrix
2. Use the theorem
A is an orthonormal matrix of order n if and only if the column (or row) vector group of a is the orthonormal basis of R ^ n
That is, the length of the column vector is 1, and the two are orthogonal

It is proved that any invertible real matrix A can be decomposed into QT, where q is an orthogonal matrix and t is an upper triangular matrix

Do gram Schmidt orthogonalization for the column of A

How to prove that a matrix is orthogonal?

A is an orthogonal matrix
AA^T = E
A^-1 = A^T
The column vectors of a are orthogonal and the length is 1
The row vectors of a are orthogonal and the length is 1