cachematrix.R

## Computing the inverse of a square matrix can be done with the solve function in R. For example, if X is a square invertible matrix, then solve(X) returns its inverse.
##  Assume that the matrix supplied is always invertible.

## This function creates a special "matrix" object that can cache its inverse.

makeCacheMatrix <- function(x = matrix()) {
        i  <- NULL
        set  <- function(y){ 
                x <<- y 
                i <<- NULL
        }
        get  <- function() x
        setinverse  <- function(inverse) i  <<- inverse 
        getinverse  <- function() i
        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 (and the matrix has not changed),  then the cachesolve should retrieve the inverse from the cache.

cacheSolve <- function(x, ...) {
        ## Return a matrix that is the inverse of 'x'
        i  <- x$getinverse()
        if (!is.null(i)){
                message("getting cached data")
                return(i)
        } 
        data  <- x$get()
        i  <- solve(data, ...
          x$setinverse(i)
            i
}