How to write matrix inside nodes?

Just for fun....we can considered your image like a commutative diagram. PS: the structure

usetikzlibrary{decorations.markings, arrows.meta}
tikzset{
    marrow/.style={decoration={markings,mark=at position 0.55 with {arrow{#1}}}, postaction=decorate}
}

is taken from Mid-arrow tip in tikz-cd by the user @Alenanno.

documentclass[a4paper,12pt]{article}
usepackage{mathtools,amssymb}
usepackage{tikz-cd}
usetikzlibrary{decorations.markings, arrows.meta}
tikzset{
    marrow/.style={decoration={markings,mark=at position 0.55 with {arrow{#1}}}, postaction=decorate}
}
begin{document}
begin{tikzcd}[row sep=1pt, column sep=normal]
 & left {begin{array}{cc}
x =  y 
A =  B end{array} right.
left {begin{array}{cc}
x =  y 
A =  B end{array} right. ar[rd, marrow=>,"fneq 0"'{sloped, pos=0.5},no head] ar[ru,marrow=>,"f=0"{sloped, pos=0.5},no head] &   
 & left {begin{array}{cc}
x =  y 
A =  B end{array} right.
end{tikzcd}

end{document}