The question is
Show that if I in M2(R) contains ( 1 0 ), then I=M2(R)
0 0
I know the fact that if I contains some unit then it would be equal to the ring R.
So,
( a b ) (1 0 ) = (a 0 )
c d 0 0 c 0
(1 0 ) ( A B ) = ( A B
0 0 C D 0 0
But how can i say that this is an ideal?