My father died a month ago and left a house in Israel, far as i know there is no will. My mother and brother live in Florida...The relationship between my brother and me no good.Before my father died, he gave my brother power of attorney over the house and bank account. My question is whether " a will according the law" relevant to my case?

I am not sure what you mean by a "will according to the law." If your father did not do a Will, he has no Will. If your father resided in the State of Illinois at the time of his death, the Illinois Probate Act dictates how his estate must be handled. If he resided in another state, the laws of that state will apply. Those laws dictate who can administrate his estate, how that is done and who will ultimately receive the benefit of his estate, among other things. In Illinois, his spouse would be given priority in handling his estate if she is willing and able to initiate the probate process. Anyone could conceivably apply to the court for approval to act as the administrator, but priority will be given to people who are willing and able in the order set by statute. If you are interested in doing that or would like to understand how the law applies to your father's estate, you should contact a reputable attorney in your area or in the county in which your father passed. This answer is not intended to create an attorney/client relationship and should not be relied on as legal advice. The answer consists only of general statements. You should meet with an attorney to get specific answers to your questions and advice tailored to the specific situation.