1. ## Field

Yo. This problem is really bothering me. I could use some help.
Let F be a field and let R, the ring be the following matrix
a11=a11
a12=a12
a13=a13
a21=0
a22=a22
a23=a23
a31=0
a32=0
a33=a33
where aij is in F, the field.
Let I={(aij) in R : a11=a22=a33=0}.
Prove that R is a subring of the 3 by 3 matrix M3(F). Also show that I is an ideal of R and R/I=F x F x F.