Let ‘*’ be a binary operation defined by a*b=4ab. Find (a*b)*a

The correct option is 16a²b.

To find the value of the expression, we use the definition of the binary operation given in the problem statement.

The binary operation is defined as:

$$a*b=4ab$$

This definition tells us that the operation multiplies the first element by the second element, and then multiplies that product by 4.

We need to evaluate the following expression:

$$(a*b)*a$$

Following the standard order of operations, we first evaluate the expression inside the parentheses.

Step 1: Evaluate the term inside the parentheses:

$$a*b=4ab$$

Step 2: Substitute this result back into the original expression:

$$(a*b)*a=(4ab)*a$$

Step 3: Apply the definition of the binary operation again. Here, the first term is:
$4ab$
and the second term is:
$a$
Applying the definition, we get:

$$(4ab)*a=4\times (4ab)\times a$$

Step 4: Simplify the expression by multiplying the constants and variables:

$$4\times (4ab)\times a=16\times a\times b\times a=16a^{2}b$$

Therefore, we have:

$$(a*b)*a=16a^{2}b$$