In the present paper, we define adjoint of a Lorentzian matrix. We give a theorem to find the inverse of a matrix using adjoint of it. Also a shortcut to find the inverse of a 2x2 matrix is presented. Finally, we show that the inverse of a matrix can be found by changing the identity matrix with L-identity matrix in the augmented matrix and using Gauss Jordan elimination method. Furthermore, we introduce some new theorems related with adjoint and inverse of a matrix.