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JEE Math Practice Question

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 :

  1. A.10
  2. B.12
  3. C.13
  4. D.14

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