Matrix inversion not getri?

Hi all,
I am using CUDA LAPACK in CUDA Toolkit 12.4. I know that CUDA LAPACK does not provide getri for matrix inversion so apparently it is supposed to use getrf+getrs ans solve the system for an identity matrix as right hand side. The problem is that an identity matrix would need lots of memory i.e., as much as the coefficient matrix while only diagonals are filled with ones and this will be huge waste of memory. Does anyone know if there is more efficient way for matrix inversion using VUDA Toolkit LAPACK?
Regards,
Dan