Captain Virat Kohli's team entered the final day with hopes of a 3-1 series victory and also its first win at the SCG since 1978. But rain meant there was no play and umpires called it off early, giving India a 2-1 series win.
Bancroft was seen using sandpaper to try to rough up the ball in the Cape Town Test in March, receiving a nine-month ban from international and domestic cricket for his part in an incident that rocked the sport.
The disgraced Australian ex-captain has kept a low media profile since the scandal in South Africa. However, he's been playing Twenty20 tournaments in Canada and the Caribbean, and padding up for his Sydney club side Sutherland.
India, chasing 287 runs for victory, were dismissed for 140 in the second test match at Perth.
The International Cricket Council chief executive David Richardson says the public have made it clear that they do not want ball tampering or other forms of cheating in the sport.
Disgraced cricketer David Warner has said he accepted the 12-month ban handed down to him by Cricket Australia for his role in last month's ball-tampering scandal in South Africa.
The result ranks as Australia's second-heaviest defeat by runs, their heaviest in 90 years, and the heaviest for any team in test cricket since 1934. And that was after a ball-tampering scandal.
The usually pugnacious batsman apologised to fans, team-mates, his family and the Australian public for a ball-tampering scandal that has rocked the cricket world.
Australia's coach Darren Lehmann will step down after the fourth Test against South Africa ends. The team's captain Steve Smith returned to Australia and broke down as he took "full responsibility" for the ball-tempering plot in Cape Town.
Opening batsman Cameron Bancroft received a nine-month ban following the scandal, which has outraged fans, jolted the sponsors and prompted CA to send the trio home from South Africa.
Steve Smith, David Warner and Cameron Bancroft were involved in a ball tampering plot in the third test against South Africa on Saturday.
Australia now trails 2-1 in the series with one test to go and its proud record of having never lost a series in South Africa since 1970 is seriously under threat.
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