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# What is an orthogonal matrix?

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An orthogonal matrix is a square matrix that has a transpose identical to its inverse. The transpose of a matrix is found by swapping each element a(ij) of the matrix with the element a(ji), where i and j denote the row and column of the element, respectively.

## Keep Learning

All orthogonal matrices have inverses. The preferred method to find the inverse of an orthogonal matrix is to compute its transpose, as computing a transpose simplifies an equation that would otherwise compute the general inverse of a matrix. The set of n x n orthogonal matrices forms an orthogonal group, which is usually denoted O(n).

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