Thread: 2X2 matrices under addition using FHT

From earlier proofs, I know that the map tr: Mat2(R)-->R is a homomorphism and that the kernel of tr is defined by Ker(tr):={A is an elt of Mat2(R) such that A=2X2 identity matrix}.

Now I'm having trouble using the Fundamental Homomorphism Theorem to determine that Mat2(R)/Ker(tr) as a factor group.

Any help would be appreciated Thank you!

Originally Posted by Tracey21

From earlier proofs, I know that the map tr: Mat2(R)-->R is a homomorphism and that the kernel of tr is defined by Ker(tr):={A is an elt of Mat2(R) such that A=2X2 identity matrix}.

Now I'm having trouble using the Fundamental Homomorphism Theorem to determine that Mat2(R)/Ker(tr) as a factor group.

Any help would be appreciated Thank you!

the map is obviously onto and so your factor group is isomorphic to