Given a binary operation $\ast$ in Q defined by $a \ast b=a-b$:

$\textbf {Step 1: Checking if the operation is Commutative}$:

For an operation $\ast$ to be commutative $a\ast b = b \ast a$.

Consider $a=1, b=2 \rightarrow a \ast b = 1 - 2 = -1$, and $b \ast a = 2 - 1 = 1$.

Since $a\ast b \neq b \ast a$, $\ast$ is not commutative.

$\textbf {Step 2: Checking if the operation is Associative}$:

For an operation $\ast$ on $A$ is associative $a\ast ( b \ast c) = (a \ast b) \ast c\; \forall \; a, b, c \in A$

Consider $a=1,b=2, c=3 \rightarrow a \ast (b \ast c) = a \ast (2-3) = 1 \ast (-1) = 2$

$(a \ast b) \ast c = (1-2) \ast 3 = 1-2-3 = -4$.

Since $a\ast ( b \ast c) \neq (a \ast b) \ast c \; \ast$ is not associative