Can white mate black?

Can, sure.  But is it forced?  Nope.

with assuming that black make no mistake!

Then the answer is no.

Check it out yourself:

http://www.k4it.de/index.php?topic=egtb&lang=en

if black make no mistake white can not mate black!

I think white will always be able to block with the rook?

I liked his creativity though. 

I want really to know the certain answer

Then look it up in the link I gave you!

http://www.shredderchess.com/online-chess/online-databases/endgame-database.html

This is a 6-man database, all positions with 6 pieces (including the king, so 4 pieces other than kings) is solved, and you can see how many moves it will be mate in, or if it's a draw with perfect play (except King vs 4 pieces+king, since the answer is retty obvious)

The position is always drawn, except if white has trapped the black king inside a corner with the SAME colour as the bishop:

EDIT: See Viktor's post, he beat me by a minute.

The optimal defense is to put the K in the bishop's "wrong" corner and shuttle the bishop back and forth inbetween the squares adjacent to the king.  White can never get the Black K out of this corner, he can only stalemate.

In the given position White can't prevent this defense.  You could set up positions with the inferior K trapped on the edge of the board, or with the K in the "right" corner, where the R can win - but not here.

Yep, not a forced mate.

K+R vs K+N does not win either, even if the defense is a bit trickier - I learnt it the hard way playing against a computer a few years ago.

The side with the rook against the minor piece can even have a pawn sometimes, some positions remain drawn. But then the defense becomes incredibly harder !