The reduced form of the matrix [A  I] is

Since the lefthand side is not the identity, it follows that the matrix A is singular (has no inverse).
Note: You might instead have obtained the matrix

Although this matrix is not completely reduced (the 3,4 entry does not have its column cleared and is not a 1), you could have stopped here, since the row of three zeros on the left shows that you can never obtain the identity on the left.
Just close this window to return to the tutorial.
Lost the tutorial to which this window is attached? Press here..