diff --git a/cachematrix.R b/cachematrix.R
index a50be65aa44..ba5826e51db 100644
--- a/cachematrix.R
+++ b/cachematrix.R
@@ -1,15 +1,45 @@
-## Put comments here that give an overall description of what your
-## functions do
+## A utility for repeatedly accessing inverted matrices.
+## Computing a matrix's inverse is potentially expensive, so
+## this utility is optimized to avoid repeating the
+## computation by caching the results.
 
-## Write a short comment describing this function
-
-makeCacheMatrix <- function(x = matrix()) {
+## Example:
+## > cm <- makeCacheMatrix(m) # construct an invertable matrix
+## > cacheSolve(cm)           # computes and returns the inverse of m
+## > cacheSolve(cm)           # returns the inverse of m, avoiding recomputation
+## > cm$set(m2)               # changes the matrix, and clears the cache
+## > cacheSolve(cm)           # computes and returns the inverse of m2
 
+## Construct a matrix that can be inversed multiple times. 
+makeCacheMatrix <- function(original = matrix()) {
+    cached_inverse <- NULL
+    
+    # overrides the original matrix and clears the cached inverse
+    set <- function(replacement) {
+        original <<- replacement
+        cached_inverse <<- NULL
+    }
+    
+    get <- function() original
+    setInverse <- function(inverse) cached_inverse <<- inverse
+    getInverse <- function() cached_inverse
+    list(set = set, get = get,
+         setInverse = setInverse,
+         getInverse = getInverse)
 }
 
 
-## Write a short comment describing this function
-
+## Efficiently access the inverse of a matrix constructed with makeCacheMatrix
 cacheSolve <- function(x, ...) {
-        ## Return a matrix that is the inverse of 'x'
+    cached <- x$getInverse()
+    
+    if(!is.null(cached)) {
+        message("cached:")
+        return(cached)
+    }
+    
+    # else calculate, set and return inverse
+    i <- solve(x$get(), ...)
+    x$setInverse(i)
+    i
 }