Question

I have a procedure with no arguments that creates a matrix, but returns nothing, how can i access the matrix?

This is my code:

(define matrix
  (lambda (rows columns)
    (do ((m (make-vector rows))
         (i 0 (+ i 1)))
        ((= i rows) m)
      (vector-set! m i (make-vector columns)))))

(define Mod-matrix!
  (lambda (m i j)
    (vector-ref (vector-ref m i) j)))

(define (board) 
  (mk-w (matrix 8 8) 0 0))

(define (mk-b b l c)
  (cond ((and (< l 8) (< c 8)) (begin
                                (Mod-matrix! b l c p)
                                (mk-b b l (+ c 2))))
        ((and (>= c 8) (< l 8))(mk-b b (+ l 2) 0))
        (else (mk-w b 0 1))))

(define (mk-b b l c)
  (cond ((and (< l 8) (< c 8)) (begin
                                (Mod-matrix! b l c b)
                                (mk-w ti l (+ c 2))))
        ((and (>= c 8) (< l 8)) (mk-white b (+ l 2) 0))))

Answer 1

Your mk-w function is not returning the matrix. Try the following:

(define (mk-w b l c)
 (cond
  ((and (< l 8) (< c 8))
   (begin (Mod-matrix! b l c)
        (mk-w b l (+ c 2))
        b))
  ((and (>= c 8) (< l 8))
   (begin
    (mk-w b (+ l 2) 0)
    b))))

Note that in each case the last expression in the begin block is the matrix itself, this is because the return value of a begin block is the value of the last expression. In your post, those last expressions returned an undefined value.