a) what is a scalar?
b)name two ways in which scalar arithmetic differs from matrix arithmetic
That question is so extensive.
This may help: Scalar -- from Wolfram MathWorld
You can think about it like this...
a scalar is a number.
a matrix is a collection of a collection of numbers...like a 2d array. When you multiply scalars, it's like multiplying two numbers. when u multiply matrices, there is a specific way you must multiply them and only certain matrices can be multiplied together.
scalar multiplication is commutative (a*b=b*a) but matrix multiplication is not. small little rules like that change...
again, this is a very drilled down version.