This is because the square of the vector norm is equal to the norm of the vector square. A little embarrassed!

That is to say, you square and then take the modulus, which is the same as taking the modulus and then square.

Two identical vectors take the inner product, which is the square of the vector.

So it is equal to their respective moduli multiplied by the cosine of the included angle. Because the included angle is 0, it is equal to the square of the module.