Is it isomorphic Let G1 m 0 b 1 GL2R and G2 fm nfm n am

Let G_1 = {(m 0 b 1)} GL_2(R), and G_2 = {f_m, n|f_m, n = am + n where m 0 and m, n R}. We have G_1 G_2.

Solution

Associative algebra of 2x2 matrices is called M(2.R ) .The collection of all invertible 2x2 matrices (with entries from the field of real numbers and multiplication as its group operation) ,from this is called Linear Group GL(2,R) -- group of units for the ring M(2,R) under matrix addition and multiplication .