The inverse of a square matrix is defined and it is explained how the existence of an inverse is related to the question of whether systems of linear equations corresponding to the matrix have unique solutions. A method for determining when a matrix is invertible and, when it is, finding the inverse, is shown: this involves row operations. An explicit formula for the inverse in the 2 × 2 case is given. This is applied to IS--LM analysis, a macroeconomic application.
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