diff --git a/cachematrix.R b/cachematrix.R
index a50be65aa44..fe527d52a6b 100644
--- a/cachematrix.R
+++ b/cachematrix.R
@@ -1,15 +1,53 @@
-## Put comments here that give an overall description of what your
-## functions do
+## This script defines two functions which help you to cache the result of matrix inversion.
+## Unless the data changes the cached inverse will be returned
 
-## Write a short comment describing this function
+## Example usage:
 
-makeCacheMatrix <- function(x = matrix()) {
+# d1 <- matrix(rnorm(9), nrow=3)
+# d2 <- matrix(rnorm(9), nrow=3)
+# m1 <- makeCacheMatrix(d1)
+# s1 <- cacheSolve(m1) # the inverse is calculated
+# s2 <- cacheSolve(m1) # the cached result is returned
+# m1$set(d2)
+# s3 <- cacheSolve(m1) # the inverse is calculated again
 
-}
+## This function returns a list which contains the basic helper functions for caching and cache invalidation
+## Only the last value is cached.
 
+makeCacheMatrix <- function(x=numeric()) {
+  inv <- NULL
+  cachekey <- NULL
+  set <- function(y) {
+    x <<- y
+    inv <<- NULL
+  }
+  get <- function() x
+  setcachekey <- function(ck) cachekey <<- ck
+  getcachekey <- function() cachekey
+  setinv <- function(newInv) {
+    inv <<- newInv
+  }
+  getinv <- function() inv
+  list(set=set,get=get,setinv=setinv,getinv=getinv,getcachekey=getcachekey,setcachekey=setcachekey) 
+}
 
-## Write a short comment describing this function
+## This function returns the inverse of the matrix
+## To do this it first checks if it needs to (re)calculate the inverse: the inverse has not been calculated
+## yet or the backing matrix has changed.
 
 cacheSolve <- function(x, ...) {
-        ## Return a matrix that is the inverse of 'x'
+  inv <- x$getinv()
+  if (!is.null(x$get()) && !is.null(x$getcachekey()) && all(x$get() == x$getcachekey())) {
+    message("Returning cached inverse matrix")
+    return(inv)
+  }
+  # We get here if the cache was never calculated
+  # OR if the matrix was changed
+  matrix <- x$get()
+  inv <- solve(matrix, ...)
+  x$setinv(inv)
+  x$setcachekey(matrix)
+  inv
 }
+
+