- #1

kathrynag

- 598

- 0

## Homework Statement

Let H be the subset of [tex]M_{2}(\Re)[/tex] consisting of all matrices of the form

[tex]\left[a[/tex][tex]\right]-b[/tex]

[tex]\left[b[/tex][tex]\right]a[/tex] for a, b elements of the reals.

1. Show that <complex, +> is isomorphic to <H,+>

2. Show that <complex, .> is isomorphic to <H,.>

## Homework Equations

## The Attempt at a Solution

Ok, so I need to show one to one and onto.

Then I need to show that [tex]\varphi[/tex](x+y)=[tex]\varphi[/tex](x)+[tex]\varphi[/tex](y)

Ok I'm having problems in what to use for [tex]\varphi[/tex] and I'm not entirely sure I remember matrix addition. Also, how do I define the complex - a+ib or just ib?