Matrices And Determinants

Let A and B be two square matrices of order 2. If \(det\,(A) = 2\), \(det\,(B) = 3\) and \(\det \left( {(\det \,5(det\,A)B){A^2}} \right) = {2^a}{3^b}{5^c}\) for some a, b, c, \(\in\) N, then a + b + c is equal to :