diff --git a/cachematrix.R b/cachematrix.R
index a50be65aa44..c2ddd44005b 100644
--- a/cachematrix.R
+++ b/cachematrix.R
@@ -1,15 +1,77 @@
-## Put comments here that give an overall description of what your
-## functions do
-
-## Write a short comment describing this function
+# Matrix Inversion Caching Functions
+# This script implements two functions for caching matrix inversions:
+# 1. makeCacheMatrix: Creates a special matrix object that can cache its inverse
+# 2. cacheSolve: Computes the inverse of the special matrix, using cached values when available
 
+#' Create a special matrix object that can cache its inverse
+#'
+#' This function returns a list of functions that can:
+#' - set the matrix value
+#' - get the matrix value
+#' - set the inverse matrix
+#' - get the inverse matrix
+#'
+#' @param x A square invertible matrix
+#' @return A list of functions to interact with the matrix and its cached inverse
 makeCacheMatrix <- function(x = matrix()) {
-
+  # Initialize the inverse as NULL
+  inv <- NULL
+  
+  # Function to set the matrix
+  set <- function(y) {
+    x <<- y       # Store the new matrix in the parent environment
+    inv <<- NULL  # Reset the cached inverse when matrix changes
+  }
+  
+  # Function to get the matrix
+  get <- function() x
+  
+  # Function to set the inverse
+  setInverse <- function(inverse) inv <<- inverse
+  
+  # Function to get the inverse
+  getInverse <- function() inv
+  
+  # Return a list of functions
+  list(set = set,
+       get = get,
+       setInverse = setInverse,
+       getInverse = getInverse)
 }
 
-
-## Write a short comment describing this function
-
+#' Compute the inverse of a special matrix created by makeCacheMatrix
+#'
+#' This function computes the inverse of the matrix. However, if the inverse has
+#' already been calculated (and the matrix has not changed), then it retrieves
+#' the inverse from the cache to avoid redundant computation.
+#'
+#' @param x A special matrix object created with makeCacheMatrix
+#' @return The inverse of the matrix
 cacheSolve <- function(x, ...) {
-        ## Return a matrix that is the inverse of 'x'
+  # Try to get the cached inverse
+  inv <- x$getInverse()
+  
+  # If the inverse is already calculated, return it with a message
+  if(!is.null(inv)) {
+    message("getting cached data")
+    return(inv)
+  }
+  
+  # Otherwise, get the matrix and calculate its inverse
+  data <- x$get()
+  
+  # Calculate the inverse using solve()
+  inv <- solve(data, ...)
+  
+  # Cache the inverse for future use
+  x$setInverse(inv)
+  
+  # Return the inverse
+  return(inv)
 }
+
+# Example usage:
+# m <- matrix(c(1,2,3,4), nrow=2, ncol=2)
+# cm <- makeCacheMatrix(m)
+# cacheSolve(cm)  # Calculates and returns inverse
+# cacheSolve(cm)  # Returns cached inverse