Is a wife considered irrevocably divorced after her husband said to her during a quarrel: "You are divorced," once?

If this divorce is the first or second, your wife is still under your marital bond, and you have the right to take her back as long as she is within her waiting period (iddah (definition)). The return (to the marriage) is effected by your saying: "I have taken my wife back," and it is preferable to have witnesses to this. You both must live together in kindness, and the wife must recognize her husband's rights. If she oversteps the boundaries, follow the Islamic means of reconciliation.