How to get matrix of coefficients from a set of linear equations?

Questions
1

Given a set of linear equations, say

2 A[2] + 3 A[3] == 4

5 A[1] + 7 A[2] == 6

How do I program Mathematica to get the matrix

{{0,2,3},{5,7,0}}

and the vector

{4,6}

?

Thank you!

2

In[2]:= Normal[CoefficientArrays[{2 A[2] + 3 A[3] == 4, 5 A[1] + 7 A[2] == 6}, {A[1], A[2], A[3]}]]

Out[2]= {{-4, -6}, {{0, 2, 3}, {5, 7, 0}}}
3

Thank you!