Identify the minimum number of rows in a matrix meeting a condition

This solution uses the Optimization Toolbox, although I am still only half certain what row-selection rule you are looking for

 [m,n]=size(A);
 
 irp=1:m;
 rp=randperm(m); %row permutation
 irp(rp)=irp;    %inverse permutation
 
 Ap=A(rp,:);

 x=optimvar('x',[1,m],'LowerBound',0,'UpperBound',1,'Type','integer');
 
 prob=optimproblem('Objective',sum(x));
 prob.Constraints=(x*Ap>=ones(1,n));
 
  sol=solve(prob);

  selection=find(round(sol.x(irp)));