Let A be an m×n matrix. Show that by means of a finite number of elementary row and/or column operations one can pass from it to a matrix R which is both 'row-reduced echelon' and 'column-reduced echelon,' i.e., Rij=0 if i=j, Rii=1, 1≤i≤r, Rii=0 if i>r. Show that R=PAQ, where P is an invertible m×m matrix and Q is an invertible n×n matrix.