Question on Arrays Code

Hi. I was looking at implementing some matrix functions and have some questions on style and efficiency. My use of arrays is limited, so it took me a few hours to come up with this :

(defun mult-arrays (&rest arrays)
  (let ((temp-array (make-array (array-dimension (car arrays) 0) :initial-element 1))) ;; use temporary array as accumulator 
    (dolist (aX arrays)
      (dotimes (i (array-dimension aX 0))
	     (setf (aref temp-array i) (* (aref temp-array i) (aref aX i)))))
    temp-array))

(mult-arrays #(23 45 17 9 27))                ;==> #(23 45 17 9 27)

(mult-arrays #(12 3 0 8) #(2 3 8 12))         ;==> #(24 9 0 96)

And yes, I know I need to implement bounds checking... My concern is are there better solutions for this? Thanks.

One of my first attempt would look like this, it depends on its intention (the performance aspect, etc.).

(defun scalar-product (a b)
  (dotimes (index (array-dimension a 0) a)
    (setf (aref a index) (* (aref a index)
                            (aref b index)))))

(defun mult-arrays (&rest arrays)
  (when arrays (reduce #'scalar-product arrays)))