Statement I:  ${\sigma }_{1s}^{*}$ has higher energy than σ_2s orbital.
Statement II :  Any antibonding orbital has higher energy than any bonding orbital.

In (ABMO) a nodal plane is present between the nuclei of  bonded  atoms leading to repulsions
No nodal plane between the nuclei of two bonded atoms in BMO
Energy of ABMO > Energy of BMO (involving same orbital)
Energy of: ${\sigma }_{1s}\mathit{<}\mathit{ }{\sigma }_{1s}^{*}\mathit{<}\mathit{ }{\sigma }_{2s}\mathit{<}\mathit{ }{\sigma }_{2s}^{*}$

I and II are false