IsLowerTriangularMat( mat )
mat  must be  a matrix.  This  function  returns true if all  entries
 mat[i][j] with ji   are   equal  to 0*mat[i][j]   and    false
 otherwise.
    gap> a := [ [ 1, 2 ], [ 3, 1 ] ];;
    gap> IsLowerTriangularMat( a );
    false
    gap> a[1][2] := 0;;
    gap> IsLowerTriangularMat( a );
    true 
GAP 3.4.4