Least squares why $||Ax-b||^2_2=(Ax-b)^T(Ax-b)$

Question

Could someone explain the why the following equality holds?

I am trying to learn this subject alone, and haven't found a good resources to explain why the following is true?

$||Ax-b||^2_2=(Ax-b)^T(Ax-b)$

Thank you!

Answer 1

Recall that

$$\vec x^T \vec x=\langle\vec x,\vec x\rangle=\sum x_i^2=\|\vec x\|^2$$