Is Shakespeare's Macbeth a tragedy?

A tragedy is the recounting of the tragic events leading up to the fall or death of the protagonist, who starts out on top and takes a tragic downfall. Therefore Shakespeare's Macbeth is a tragedy because it traces through many events, the fall of Macbeth, who starts out from a high position. Macbeth starts out on top when the Thane of Glamis dies making him the new king. In hearing his prophecies, one of which …

…anything he does will not change the fact that he is going to die. Macbeth is similar to Lady Macbeth, just not necessarily at the same time. They both think that water will wash away the blood on their hands. Also they both keep their thoughts from each other and from other people. They both end up completely different from the way they started. These are some ways that Macbeth and Lady Macbeth are similar.