## pair of functions that cache the inverse of a matrix to avoid costly computations

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

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

inverse <- NULL

get <- function()x

set <- function(y)

{

x <<- y

inverse <<- NULL

}

getInverse <- function()inverse

setInverse <-function(z)inverse<<-z

list(get = get, set = set, getInverse = getInverse, setInverse = setInverse)

}

## cacheSolve: 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, ...) {

inverse <- x$getInverse

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

if( !is.null(inverse))

{

message("getting cached data")

return(inverse)

}

matrx <- x$get()

mat <- solve(matrx,...)

x$setInverse(mat)

mat

}