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## Homework Statement

Find a basis for each of the spaces and determine its dimension:

The space of all matrices A=[a b, c d] (2x2 matrix) in R^(2x2) such that a+d=0

## Homework Equations

## The Attempt at a Solution

So I jumped at this question without knowing too much about spaces and dimensions, but:

I think a possible combination of basis can be: [1 0, 0 0]. [0 1, 0 0]. [0 0, 1 0] (not sure if [0 0, 0 -1] would be considered since d would be negative in this case) Also from that I assume the dimension is 3?

Truthfully even if I got it right, I do not even know what happened. Can someone conceptually tell me what I am doing exactly?

Thanks in advance.