Solution 11960: Finding the Row Echelon Form of a Matrix on a TI-83 Family, TI-84 Plus Family, or TI-Nspire™ Handheld in TI-84 Plus Mode.
How do I find the Row Echelon form of a matrix on a TI-83 family, TI-84 Plus family, or TI-Nspire handheld in TI-84 Plus mode?
To find the Row Echelon form of a matrix, input the
matrix, exit the matrix editor, and then paste the ref() function on the
home screen with the name of the matrix. The example below will
demonstrate this procedure.
Note: To access the Matrix menu on the TI-83 press the [MATRX] key. On the TI-83 Plus family, TI-84 Plus family, or TI-Nspire handheld in TI-84 Plus mode press [2nd][x^-1].
Example: Find the ref() of matrix [A]
To enter the matrix:
• Press [2nd] [(MATRIX)] Note: Press the [MATRX] key on the TI-83.
• Scroll to Edit
• Press  to access matrix A
• Input the dimensions  [ENTER]  [ENTER]
• Input the matrix entries, pressing enter after each entry
• Exit the matrix editor by selecting [2nd] [QUIT]
To find the row echelon form using the ref( function:
• Press [2nd] [MATRIX]
• Scroll to MATH
• Press [ALPHA] [A] [2nd] [MATRIX] 
Please see the TI-83 family and TI-84 Plus family guidebooks for additional information.NOTE: TI-Nspire users may refer to the TI-84 Plus family guidebook.