Row Reduction, also called Gaussian elimination or Gaussian Reduction, is a method for solving a system of equations. In order to solve a matrix one must use elementary row operations in order to reduce a matrix to Reduced Row Echelon Form.
Examples on how to preform Row Reduction can be found below:
Gauss Jordan is a method of row reduction the employs the use of an identity matrix to find the matrix's inverse.
This method is used in inverse matrix examples 1 and 2, linked below: