MATRIX GROUPS

Addition

The set of 2x2 matrices, ,form an infinite commutative group under addition.
The identity element is and the inverse of an element is given by .

Multiplication

The set of 2x2 matrices,, excluding those where , forms an infinite non-commutative group under matrix multiplication.

The identity element is . The inverse of an element is given by .

EXERCISE

1. Why are matrices for which excluded from the group of 2x2 matrices under matrix multiplication?
   Answer
2. Find the inverse of under (i) matrix addition (ii) matrix multiplication.
   Answer
   
3. If and find      (i) AB     (ii) BA.
   Is the group of 2x2 matrices under matrix multiplication commutative? Give a reason for your answer.
   Answer.