Answer to Question #47360 in Abstract Algebra for ayush kumar

Question

a) Let Z2 be the field with 2 elements .Let G denote the set of all 3 x 3 matrices of the form
( 1 0 a )
( 0 1 b )
(0 0 1)
with a, b e 22. Show that G is a group of order 4 with respect to matrix multiplication .

( b ) (i) let f :R -> S be an onto ring homomorphism. Show that if I is an ideal of R, then f(I) is an ideal of

(il) If f were not onto, would f(l) still be an ideal of S ? Give reasons for your answer,