I was going through Strang lecture on Projection Matrices while having dinner. I am amazed at the information content in those lectures.

Projection Matrix is Idempotent meaning P^2 = P. Strang in his lecture said that it was an obvious statement. Becoz if you project the already projected matrix. you get the same projection matrix WOW

That is why P to the power of any number gives you back P becoz the first P projects it to the column space and then there is no need for any other projection..

Strang Rocks!