We use the identity matrix to calculate a the inverse of a square matrix. In order to be invertible, a matrix must be square. By finding the square matrix inverse, we can find the solution of a system of linear equations. A square matrix inverse, when multiplied on the left or right by the original matrix gives us the identity matrix.
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[...] general linear group of invertible 2-by-2 matrices, and even this group is not fully understood! …Inverse of a Square Matrix | ClassBrain MathWe use the identity matrix to calculate a the inverse of a square matrix. In order to be invertible, [...]
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