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matrix, a matrix is invertible if and only if its row-reduced echelon form is the identity matrix. The reason is that this is the only row-reduced echelon matrix having full rank: all ones down the diagonal and zeros everywhere else.

Another criterion is that a matrix is invertible if and only if its determinant is non-zero.

Methods of matrix inversion

There are many methods to compute the inverse matrix, when it exists. A basic method is to use Gaussian elimination,

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