cachematrix.R

## makeCacheMatrix: Creates a special "matrix" object that can cache its inverse.
## cacheSolve: This function computes the inverse of the special "matrix" returned 
## by makeCacheMatrix above.
## However, if the matrix does not change and the inverse has already been 
## calculated, then it retrieves the value from the cache
## By doing so, computer reources are saved

## makeCacheMatrix: Creates a special "matrix" object
## that can cache its inverse.

makeCacheMatrix <- function(x = matrix()) {
      m <- NULL                                       ##initializing as NULL
      set <- function(y)  {                           ##defining the set function
            x <<- y
            m <<- NULL
      }
      get <- function() x                             ##returns x
      setinverse <- function(solve) m <<- solve       ##solve used to calculate inverse
      getinverse <- function() m                      ##returns m
      list(set = set, get = get,                      ##list
           setinverse = setinverse,
           getinverse = getinverse)
}


##The following function computes the inverse of the special "matrix" returned by makeCacheMatrix above. 
##If the inverse has already been calculated (and the matrix has not changed), 
##then the cachesolve should retrieve the inverse from the cache.

cacheSolve <- function(x, ...) {
      
      m <- x$getinverse()
      if(!is.null(m)) {             ##Checking whether inverse already calculated or not
            message("getting cached data")
            return(m)
      }
      data <- x$get()
      m <- solve(data, ...)
      x$setinverse(m)
      m                             ## Returns a matrix that is the inverse of 'x'
}