Find a and b if :solution exists, solution doesn't exist, solution is unique, etc

x-y+z=b

-x+ay+2z=1

2x-2y+z=1

I've used row reduction and I just want to verify my answers (got this problem wrong on a test)

infinitely many solutions- a=1 and b=.5

no solutions- b=/.5

unique solution- a=/1 b=.5

thanks

edit- fixed with last solution