4.3 how to test if all elements of a matrix are integers?

restart; 
m:=Matrix( [[1.3,2,3],[3,4,4] ]); 
matrixTestQ := proc(m::Matrix) 
 
    local r,c,i,j; 
 
    (r,c):=LinearAlgebra[Dimensions](m); 
    for i from 1 to r do 
       for j from 1 to c do 
           if( not evalb( whattype(m[i,j]) = integer) )  then 
               return(false); 
            end if; 
        end do; 
    end do; 
 
    return true; 
end proc; 
 
>matrixTestQ(m); 
 
               false
 

I am sure there is a better way than the above. Need to find out.