Linear System solve y=Ax+B (Find uknown matrix A and vector B)

I got a linear system : *Z'=A*Z+B

3 Known points (x1,y1)(x2,y2)(x3,y3) stored in matrice Z=[x1 x2 y2 ; y1 y2 y3]

And i want to find affine transform . I want to find A=[a11,a21,a31;a12 a22 a32] ,and B=[b1,b2]

So that i can calculate Z'. How can i find A,B in matlab? Why i need exactly 3 points to estimate A and B? thanks in advance