An inverse matrix is a special type of matrix that, when multiplied by the original matrix, results in the identity matrix. The identity matrix acts like the number 1 in regular multiplication, meaning that it does not change the value of other matrices when multiplied. Not all matrices have inverses; only square matrices (matrices with the same number of rows and columns) that are non-singular (having a non-zero determinant) can have an inverse. To find the inverse of a matrix, various methods can be used, such as the Gauss-Jordan elimination or calculating the adjugate and dividing by the determinant. The inverse matrix is useful in solving systems of linear equations, as it allows for the calculation of variable values directly.