need help with part c

Question 5 Consider the following mathis over SIS (a) [3 Marks] Show that A is orthogonal (b) [6 Marks] Let Pa ( R) denote , the vector space of all polynomials of degree two OF loin ever the field of real numbers. Consule, the following inner product on A,(#) where p() - co . air soar, () - but but bar, Show that g = (1, s, o') formin an orthonormal basis of P, (R) will respect to the above inner product, (c) [5 Marks] Determine the isometry : B,(R) - R' induced by A, where P. (R) is equipped with the inner product given in part (1) and R is endowed with the Euclidean inner product. Consider the basis (1. .. .] for P.(R) and (erez, es ) for R