## Two functions below is to calculate inverse matrix passed

## to makeCacheMatrix function. Once the inversion of matrix is

## calculated, the inversed matrix is cached into memory.

## If the cached inversion matrix is found, the cached matrix will be

## returned instead of recalculating the inversed matrix again.

## This function is to make a list of four functions which

## are related to inversion of matrix.

## input : inversible matrix

## output : special matrix whch can cache a inversed matrix

makeCacheMatrix <- function(x = matrix()) {

inv <- NULL

set <- function(y) {

x <<- y

inv <<- NULL

}

get <- function() x

setinverse <- function(inverse) inv <<- inverse

getinverse <- function() inv

list(get=get, set=set, getinverse=getinverse,

setinverse=setinverse)

}

## This function is to return inversed matrix from the given

## special list returned from makeCacheMatrix().

## If the inversed matrix is found in cache, it will return.

## Otherwise, it will calculate inversed matrx and return it

## after cacheing it.

cacheSolve <- function(x, ...) {

## Return a matrix that is the inverse of 'x'

m <- x$getinverse()

if (!is.null(m)) {

message("getting cached data")

return(m)

}

data <- x$get()

m <- solve(data,...)

x$setinverse(m)

m

}