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# What Is an Orthogonal Matrix?

**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.

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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## What Is the Inverse of 2x2 Matrix?

A: The inverse of a 2x2 matrix is the matrix that results in the identity matrix when multiplied by the first matrix. The values for the inverse of a 2x2 matr... Full Answer >Filed Under: -
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## What Is the Inverse of a 2x2 Matrix?

A: The inverse of a two-by-two matrix is another two-by-two matrix that, when multiplied by the original matrix, gives the identity matrix. Gauss-Jordan elimi... Full Answer >Filed Under: -
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## What Is a Singular Matrix?

A: A singular matrix, also called degenerate matrix, is a square matrix whose determinant is zero and that doesn't have a matrix inverse. It's rare to come ac... Full Answer >Filed Under: -
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## What Is the Equation for Inverse Variation?

A: The general formula for inverse variation is k equals y times x, where k is a constant quantity, y is one variable and x is another variable. Under inverse... Full Answer >Filed Under: