Matrix manipulation of a 33 matrix

A. Elementary Matrices

(a) Compose a 33 matrix with random elements, and assign as matrix A.

(b) Premultiply A with elementary matrix with row operations

(c) Keep doing the previous step until you get an echelon matrix.

B. Pivot Matrices

(a) Compose a 33 matrix with random elements, and assign as matrix A.

(b) Premultiply [A|I] with pivot matrix with column operations

(c) Keep doing the previous step until you get an identity matrix for A, that is, [I|A 1 ].