Herstein's abstract algebra: Chapter 4 section 3 number 19

If R = {( a b ) | a, b, c real} and I = {( 0 b ) | b real }

.........{( 0 c ) |.................}..............{( 0 0 ) |...........}

values in between the {} are matrices.

Show that:

(a) R is a ring

(b) I is an ideal of R

(c) R/I ≈ F ⊕ F, where F is the field of real numbers