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Some properties of idempotent matrix and involutory matrix?

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P

is involutory matrix and

Q

is idempotent matrix and

P Q = P,

P Q^{100} + P^{100} Q =

Q. A square matrix

A

is said to be an idempotent matrix if

A^{2} = A

A

B

are idempotent matrices and

A B = B A

, 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

A

is a non-singular idempotent matrix, then

P

is an orthogonal matrix and

Q = P A P^{T}

B = P^{T} Q^{1000} P

B^{- 1}

A

is involutory matrix,

Q. A square matrix

A

is said to be an idempotent matrix if

A^{2} = A

A, B

A + B

are idempotent matrices, then

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