diff --git a/Completed Programming Assignment 2.R b/Completed Programming Assignment 2.R
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+## This function creates a special "matrix" object that can cache its inverse.
+makeCacheMatrix <- function(x = matrix()) {
+  inv <- NULL  # Initialize the inverse as NULL
+  
+  # Setter function to update the matrix
+  set <- function(y) {
+    x <<- y
+    inv <<- NULL  # Reset inverse when a new matrix is set
+  }
+  
+  # Getter function to return the matrix
+  get <- function() x
+  
+  # Setter function for the inverse
+  setInverse <- function(inverse) inv <<- inverse
+  
+  # Getter function for the inverse
+  getInverse <- function() inv
+  
+  # Return a list containing all four functions
+  list(set = set, get = get,
+       setInverse = setInverse,
+       getInverse = getInverse)
+}
+
+
+## This function computes the inverse of the special matrix returned by makeCacheMatrix above.
+## If the inverse has already been calculated, it retrieves it from the cache instead of recomputing.
+cacheSolve <- function(x, ...) {
+  inv <- x$getInverse()
+  
+  # Check if inverse already exists
+  if (!is.null(inv)) {
+    message("Getting cached inverse")
+    return(inv)
+  }
+  
+  # Otherwise, calculate the inverse
+  mat <- x$get()
+  inv <- solve(mat, ...)  # Compute the inverse using R's 'solve' function
+  x$setInverse(inv)       # Cache the inverse for later use
+  inv                     # Return the computed inverse
+}