diff --git a/cachematrix.R b/cachematrix.R
index a50be65aa44..685590dfb90 100644
--- a/cachematrix.R
+++ b/cachematrix.R
@@ -1,15 +1,62 @@
-## Put comments here that give an overall description of what your
-## functions do
-
-## Write a short comment describing this function
-
-makeCacheMatrix <- function(x = matrix()) {
+## This file contains a pair of R functions that cache the inverse of a matrix.
+## This is part of a peer assessment for the second programming assignment in the Coursera "R Programming" course.
 
+## The function makeCacheMatrix creates a special "matrix object", which is really a list containing 
+## a function to set the matrix; 
+## a function to get the matrix;
+## a function to set the inverse of the matrix; 
+## a function to  get the inverse of the matrix.
+ makeCacheMatrix <- function(x = matrix()) {
+ 
+	 ## 0. nulls the inverse matrix 
+	 m <- NULL
+	 
+	 ## 1. definition the function that sets the matrix
+	 set <- function(y) {
+		 x <<- y
+		 m <<- NULL
+	 }
+	 
+	 ## 2. definition the function that gets the matrix
+	 get <- function() x
+	 
+	 ## 3. definition the function that sets the inverse of the matrix
+	 setinverse <- function(solve) m <<- solve
+	 
+	 ## 4. definition the function that gets the inverse of the matrix
+	 getinverse <- function() m
+	 
+	 ## returns the list of functions defined above
+	 list(set = set, get = get,
+		  setinverse = setinverse,
+		  getinverse = getinverse)
 }
 
 
-## Write a short comment describing this function
+## The function cacheSolve checks to see if the inverse matrix has already been calculated. 
+## If not, it  gets the inverse matrix from the cache. 
+## Otherwise, it calculates the inverse matrix of the special "matrix object" created with the above function and returns it.
+## The argument should be a "matrix object" of the type defined above
+ cacheSolve <- function(x, ...) {
 
-cacheSolve <- function(x, ...) {
-        ## Return a matrix that is the inverse of 'x'
+	 ## 0. gets the inverse matrix from the "matrix object" x
+	 m <- x$getinverse()
+	 
+	 ## 1. if the inverse matrix already exists, returns it
+	 if(!is.null(m)) {
+		 message("getting cached data")
+		 return(m)
+	 }
+	 
+	 ## 2. otherwise, gets the matrix from the "matrix object"
+	 data <- x$get()
+	 
+	 ## 3. calculates the inverse matrix
+	 m <- solve(data, ...)
+	 
+	 ## 4. saves the calculated inverse matrix in the "matrix object"
+	 x$setinverse(m)
+	 
+	 ## 5. return the inverse matrix
+	 m
 }