Using rref to give the inverse of a square matrix A

Suppose A is an nxn matrix and I is the nxn identity matrix.

I = [ 1 0 0 ... 0 ]
    [ 0 1 0 ... 0 ]
    [ 0 0 1 ... 0 ]
    [ . . . .   . ]
    [ . . .  .  . ]
    [ . . .   . . ]
    [ 0 0 0 ... 1 ]

(I = eye(3,3) will make I the 3x3 identity matrix in scilab)

The inverse of A, written A^(-1) has the
property that A*A^(-1) = A^(-1)*A = I

Not all matrices have inverses, for example [ 2 1 ] does not.
                                            [ 4 2 ]

To use rref to find inverses, we augment (A | I) and rref the
resulting n x 2n matrix. If the resulting matrix looks like
(I | B) then B = A^(-1). If there are fewer than n pivots, 
in the first n columns, A does not have an inverse.

Typical problem given A and A*C find C. Solution: use the above
method to find A^(-1) and multiply AC on the left by the inverse.
A^(-1)*(A*C) = (A^(-1)*A)*C = I*C = C.

Often, for matrices, AB not= BA. So this usually means (A*C)*A^(-1)
will not be C.

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Scilab commands to do scilab3.
	exec('filename')
	inv(A) = A^(-1) is the inverse of the matrix A
	eye(3,3) is the 3x3 identity matrix