# Week 3

## Session 1

### Pre-class exercises

Exercise:

Prove that if X if an n-by-n matrix with zeros everywhere except a 1 in the i jth entry (i not equal to j) then det of exp X equals exp of trace X.

## Session 2

### Pre-class exercises

Exercise:

We constructed a homomorphism R from SU(2) to O(3). Can you see why R lands in the subset SO(3) of matrices with determinant 1?

Exercise:

Can you prove that little s u 2 is the set of 2-by-2 matrices X such that X transpose equals minus X and trace of X equals 0?