Demonstrate given function is an inner product

Question

Questions:

1. Demonstrate (check the properties) that the following function is an inner product in R^3. (Call R^3 with this inner product Moorean 3-space). Let u=(u_1,u_2,u_3) and v=(v_1,v_2,v_3). Then

= uAv^T, where A=[ 2 0 0 ]
                                          [ 0 1 0 ]
                                          [ 0 0 2 ]. Show work.

Help:[ 2 0 0 ]
         [ 0 1 0 ] : is a 3 x 3 matrices.
         [ 0 0 2 ]