Step 1:

If in an LPP,where $Z=ax+by$ is the objective function,then $Z$ has same maximum value on two corner points,then every point on the line segment joining these two points has the same maximum.

Step 2:

Maximum value of the objective function $Z=ax+by$ in a LPP always occur at only one corner point of the feasible region.

Hence it is a False statement.