(a) Find the inverse of the following matrix, in terms of a.For what value of a is this matrix singular?
(b) Consider the three-commodity market model defined by:By making use of your answer to part (a), or otherwise, find the equilibrium prices.

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4 -2 -1 -2 5 1 -4 Os, = 2P, – 7; Qp, = -2P, + 2P, + P3 + 16 Os, = 4P, – 4; Qn, = 2P, – P, – P3 + 8 Os, = 2P, – 3; Qo, = 4P, – P2 - 4P, + 4