Exercise 0.1.3(Stability for product)

Question

Prove that if $P, Q \in \mathcal B$, then $P \cdot  Q \in \mathcal B$.

Abdullah Zubair · Accepted Answer

Let $P, Q \in \mathcal B$. Then
\begin{align*}
	(PQ)(M) &= (P)(QM)\
	&= (P)(MQ)\
	&= (PM)(Q)\
	&= (MP)(Q)\
	&= (M)(PQ)
.\end{align*}

Answers