If a and B are unit vectors, why is a square equal to b square?

If a and B are unit vectors, why is a square equal to b square?

The unit vector is a vector of length one
a. B is the unit vector,
Then | a | = 1, | B | = 1
a^2=a·a=|a|^2=1
b^2=b·b=|b|^2=1
∴a^2=b^2