What do you get if you multiply your matrix with its supposed inverse matrix?
If you get the identity matrix, you're done.
As for the <br/>, they come from a deficiency in the latex engine of this site.
They occur when you put a new line in a latex expression.
The workaround is to put the entire latex expression on one line.
Or otherwise, if you latex expression is suitable for it, splitting up the latex expression in multiple latex expressions that each consist of one line.