Is Any Square Matrix a Linear Operator?

[jinksys]

Homework Statement

Verify that any square matrix is a linear operator when considered as a linear transformation.

Homework Equations

The Attempt at a Solution

If a square matrix A\inℂ^{n,n} is a linear operator on the vector space C^{n}, where n ≥ 1, then the square matrix A is of the correct dimension to be a linear transform from C->C.

 

[HallsofIvy]

Except for the rather trivial statement about dimension, I see no attempt at this problem- the question is to show that it is linear.

 

[jinksys]

Could I get a push in the right direction?

 

[Deveno]

show it preserves sums and scalar multiples...