Yes, you can.
Please note that Autofocus is only available when using Alpha lenses with a build in AF-drive (SSM/SAM type).
The LA-EA1 supports the APS-C capture format only. When using this adapter on a 35mm full-frame E-mount camera, vignetting will occur. Use the LA-EA3 or LA-EA4 in that case, which support the 35mm full-frame format.
NOTE: If you are using the NEX-3 or 5 or the NEX-VG10, a firmware update for the lens and/or the adapter is required.