df.unique() on whole DataFrame based on a column

It seems you need DataFrame.drop_duplicates with parameter subset which specify where are test duplicates:

#keep first duplicate value
df = df.drop_duplicates(subset=['Id'])
print (df)
       Id Type
Index         
0      a1    A
1      a2    A
2      b1    B
3      b3    B

#keep last duplicate value
df = df.drop_duplicates(subset=['Id'], keep='last')
print (df)
       Id Type
Index         
1      a2    A
2      b1    B
3      b3    B
4      a1    A

#remove all duplicate values
df = df.drop_duplicates(subset=['Id'], keep=False)
print (df)
       Id Type
Index         
1      a2    A
2      b1    B
3      b3    B