Some properties of idempotent matrix and involutory matrix?

Q. If $P$ is involutory matrix and $Q$ is idempotent matrix and $PQ=P,$ then $P{Q}^{100}+P^{100}Q=$

Q. Let matrix $A$ be an idempotent matrix and $B$ be a matrix such that $A+B=l.$
Statement-1 : B is an idempotent matrix. and
Statement-2 : $AB=BA=0.$

Q. A square matrix $A$ is said to be an idempotent matrix if $A^2=A$. If $A$ and $B$ are idempotent matrices and $AB=BA$, then which of the following is an idempotent matrix

Q. A square matrix $A$ is said to be an idempotent matrix if $A^2=A$. If $A$ is a non-singular idempotent matrix, then

Q. If $P$ is an orthogonal matrix and $Q=PA{P}^T$ and $B=P^T{Q}^{1000}P$, then $B^{-1}$ is, where $A$ is involutory matrix,