Help with Last Part of Assignment

[rohan03]

i have typed and attached my question and my attempt here with. I am sure I know what I am doing but its a last part I am not sure about so any help would be great.

Thanks

 

[HallsofIvy]

Looking at the second, bH, row, of course, bH*eh= bH is, of course, first. Then 'bH*bH' requires that you 'multiply' {b, g}*{b, g}= {b*b, b*g, g*b, g*g}= {a, e, e, a}= {a, e}= eH. 'bH*cH' is {b, g}*{c, h}= {d, f}= dH. 'bH*dH'= {b, g}*{d, f}= {c, h}= cH.

 

[rohan03]

Looking at the second, bH, row, of course, bH*eh= bH is, of course, first. Then 'bH*bH' requires that you 'multiply' {b, g}*{b, g}= {b*b, b*g, g*b, g*g}= {a, e, e, a}= {a, e}= eH. 'bH*cH' is {b, g}*{c, h}= {d, f}= dH. 'bH*dH'= {b, g}*{d, f}= {c, h}= cH.

many thanks- this clarifies everything