diff --git a/cachematrix.R b/cachematrix.R
index a50be65aa44..126b91f41ff 100644
--- a/cachematrix.R
+++ b/cachematrix.R
@@ -1,15 +1,61 @@
-## Put comments here that give an overall description of what your
-## functions do
+## These functions eliminate redundant calculations by allowing the user
+## to cache the inverse of a matrix after first solving for it
+## and to retrieve that inverse when needed without having to solve
+## for it again.
 
-## Write a short comment describing this function
+## This function takes a matrix as input and returns a list of functions
+## that allow the user to cache the values of the input matrix and its inverse
+## and to retrieve those same values from cache.
 
 makeCacheMatrix <- function(x = matrix()) {
-
+    inverse <- NULL
+    
+    # Define function to cache the input matrix
+    set <- function(y) {
+        x <<- y
+        inverse <<- NULL
+    }
+    
+    # Define function to retrieve the input matrix from cache
+    get <- function() {
+        x
+    }
+    
+    # Define function to cache the inverted matrix
+    setinverse <- function(invertedmatrix) {
+        inverse <<- invertedmatrix
+    }
+    
+    # Define function to retrieve the inverted matrix from cache
+    getinverse <- function() {
+        inverse
+    }
+    
+    # Return a list of the above functions
+    list(set = set, get = get,
+         setinverse = setinverse,
+         getinverse = getinverse)
 }
 
 
-## Write a short comment describing this function
+## This function takes the list output of makeCacheMatrix() as input
+## and checks to see if the inverse of the matrix has already been solved.
+## If it has, then it retrieves that value. If not, it solves for the inverse
+## and stores the value in cache.
 
 cacheSolve <- function(x, ...) {
-        ## Return a matrix that is the inverse of 'x'
+    # Retrieve cached inverse
+    inverse <- x$getinverse()
+    
+    if(!is.null(inverse)){
+        # If inverse has already been calculated, return its value from cache
+        message('getting cached data')
+        return(inverse)
+    } else {
+        # Otherwise, calculate inverse and cache it
+        matrix <- x$get()
+        inverse <- solve(matrix, ...)
+        x$setinverse(inverse)
+        return(inverse)
+    }
 }