Showing a set of matrices is a group

[bennyska]

Homework Statement

show the set of nxn diagonal matrices is a group under matrix addition

Homework Equations

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?

 

[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 $A_{ij}$.