Given a binary symmetric matrix $A$, an integer threshold $K$, function $$f(A)=A^2 \geq K$$ the $\geq$ is element-wise, so we get another binary matrix after applying $\ f$.
I want to show whether the convergence of the following holds. $$f \circ f \circ ... \circ f(A)$$
I tried all the possibilities where size of $A$ under $6$, they will all converge after applying $\ f$ twice.
I see the difficulty lies in the input which is a matrix. Any ideas about where to start to solve this problem?