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Question 1 Consider a vector space G E R2x3 of 2 x 3 matrices over R, with the usual matrix summation, multiplication and multiplication by scalars. Given matrix D E R2x2, D = we define a binary function on G as follows: for any A. B E G. = tr(A DB). where the trace operator tr gives the sum of the diagonal elements of any square matrix: .x1 XA (a) Show that g is a valid inner product on G. (b) Find an orthogonal basis for G. What is the dimension of G