Is there any software that I can use to determine whether matrix group cosets are equal?

Question

Is there any software that I can use to determine whether matrix group cosets are equal?

For instance, if I'm working with the group $SL_{2}( \mathbb{F}_{p} [[t]])$ and I want to know if $a SL_{2}( \mathbb{F}_{p} [[t]]) = b SL_{2}( \mathbb{F}_{p} [[t]]) $ where $a $ and $b$ are $2 \times 2$ matrices.

Thanks

Answer 1

Use GAP, that's what GAP does!