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Ideals in the Group Algebra C[GL(2,R)]

I was hoping to use Sage to determine whether some element is generated by given generators in the group algebra C[GL(2,R)]. However, it went completely wrong when I tried the following naive thing.

sage: G=GL(2,RR)
sage: R=GroupAlgebra(G,CC)
sage: T=R(G([[1,1],[0,1]]))
sage: I=[T-1]*R;
sage: J=[T-1,(T-1)^2]*R;
sage: I==J
False

I thought I defined the ideals in the wrong way so I tried the following as well, which worked out great.

sage: var('t')
sage: R=PolynomialRing(QQ, 't')
sage: I=[R(t)]*R
sage: J=[R(t),R(t^2)]*R;
sage: I==J
True

I was wondering whether I indeed did something wrong or this is just a bug of Sage, and whether there is a way to fix it or bypass it. Thank you so much!

Ideals in the Group Algebra C[GL(2,R)]

I was hoping to use Sage to determine whether some element is generated by given generators in the group algebra C[GL(2,R)]. However, it went completely wrong when I tried the following naive thing.

sage: G=GL(2,RR)
sage: R=GroupAlgebra(G,CC)
sage: T=R(G([[1,1],[0,1]]))
sage: I=[T-1]*R;
sage: J=[T-1,(T-1)^2]*R;
sage: I==J
False

I thought I defined the ideals in the wrong way so I tried the following as well, which worked out great.

sage: var('t')
sage: R=PolynomialRing(QQ, 't')
sage: I=[R(t)]*R
sage: J=[R(t),R(t^2)]*R;
sage: I==J
True

I was wondering whether I indeed did something wrong or this is just a bug of Sage, and whether there is a way to fix it or bypass it. Thank you so much!

EDIT: There are in fact two issues going around. When I typed this into the Sage (version 8.7) on my computer, it came out as written above. However, when I tried this on the webpage version of Sage, there is this 'is_commutative' error as mentioned by tmonteil in the comment, and I don't know how this error comes up either. In any case, it seems to be impossible to compute ideals in this group algebra.