I downloaded "java development kit" from my college computer, the computer that I used to download the software was full of virus and malware. I scanned the software with antivirus program the software was ok . I checked the software properties and there was a Digital signature on the software.

So I wanted to ask following 2 questions :
Does a digital signature on application guarantees that it has not been infected by virus or altered by any means ?
Is it possible that the digital signature remains intact even after the software get infected by virus ?