Just want to confirm the following

s:C-->R^3

a+ib-->(b,a,a+b)

Find the matrix of s with respect to the standard basis for the domain C and the standard basis for the codoaim R^3.

I have

s(a,b) = (b,a,a+b)

s(1,0) = (0,1,1), s(0,1) = (1,0,1)

The matrix of s with repect to the standard basis is

A = ( 0 1)

(1 0)

(1 0)

Is this correct?