> 
> Let $$\langle A,B \rangle = a\_{11}b\_{11}+a\_{12}b\_{12}+a\_{21}b\_{21}+a\_{22}b\_{22}.$$ Show that this in an inner product on the vector space $M\_{2x2}$?
> 
> 
> 

I just do not get how to prove this with matrices.