When a matrix is multiplied by its inverse, the resulting product is the identity matrix. Thus, the inverse of a matrix can be found by dividing the identity matrix by the matrix, resulting in the inverse of the matrix.
Only square matrices, which have an equal number of rows and columns, have an inverse. An identity matrix is a matrix that has the number one on its diagonal but zeros in every other place. For a two-by-two matrix, the inverse can be calculated by dividing one by the product of the upper-left to lower-right diagonal minus the product of the other diagonal.