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Matrix recursion

I need to construct a non linear matricial recursive system for the series of matrix $M_k$ like the following one

$M_k[i][j] = F(M_{k-1}[i][j],M_{k-1}[i][j]) \text{ for } M_0 \text{ given}$

I have read that for one dimension one can use Sympy rec. But is there a way to do it simply in Sagemath?