To a person in the early part of their mathematical studies, scalar multiplication is going to look pretty much just like regular multiplication.
When this student gets to Matrix Algebra and learns about Matrix Multiplication, then the need to knoe there’s more than one way to do multiplication becomes apparent.
We are also given the idea that we might want to generalize multiplication to something that will be true about all forms of multiplication.
The word scalar comes from the idea that it can change the scale or size of things.
Scalar multiplixmcation contrasts with matrix multiplication.
Rob Sterling 