# Showing a set of matrices is a group

1. Feb 12, 2010

### bennyska

1. The problem statement, all variables and given/known data
show the set of nxn diagonal matrices is a group under matrix addition

2. Relevant equations

3. The attempt at a solution
it doesn't say what set the entries are from, so i'm assuming it's reals.
so i need to show that there is closure, it's associative, there's an identity element, and there's an inverse. i know that there's an identity element, the matrix with just zeroes, and i know the inverse is just -A for matrix A. it's addition, so i know that it's associative, and in my head i can tell that there is closure.
my main problem is notation. how to do i actually express this? i.e., what's the general notation for a nxn matrix?

2. Feb 13, 2010

### owlpride

Here is a general diagonal nxn matrix:

$$\left( \begin{array}{c c c c} x_1 & & & \\ & x_2 & & \\ & & ... & \\ & & & x_n \end{array} \right)$$

Alternatively, you can say "let A be a diagonal nxn matrix" and index the entries with $A_{ij}$.