Nah, that well known fantasy writer Shakespeare, had so little knowledge of the real history of Scotlandd (or was such a political toady - you decide) that he invented the story.
The real lady was Grouch - and she was such a capable, trusted person that she governed her husband's kingdom while he went on pilgrimage to Rome. The only early medieval king of Alba/Scotland who felt secure enough on the throne to do so.
Far from being a nice old man, Duncan was probably younger than Macbeth when he died, not by a dagger, but in battle, Macbeth granting him a burial in Iona.
When Macbeth was killed in battle near Lumphinan (not 'Birnam wood') he was succeeeded, not by Malcolm, but by Grouoch's son, Lulach.
And there was hno Banquo or Fleance, and the witches were a sop to please James VI and I - whom Shakespeare wanted to toadt up to
All in all, total rubbish worthy of David Eddings.