If $\ast$ is a binary operation on $A=\{1,2,3,4,5\}$ defined by the table below:∗12345111111212121311311412141511115Find the value of $(3\ast 3)\ast (4\ast 4)$.

From the given binary operation table:Find $(3\ast 3)$: Look at row 3, column 3. The value is $3$.Find $(4\ast 4)$: Look at row 4, column 4. The value is $4$.Find $(3\ast 3)\ast (4\ast 4)$, which is $3\ast 4$.Look at row 3, column 4. The value is $1$.Therefore, $(3\ast 3)\ast (4\ast 4)=1$.