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Question: If A, B and C are n× n matrices and det (1) = 2, det (2) = 3 and det (3) = 5, then the value of the ...

If A, B and C are n× n matrices and det (1) = 2, det (2) = 3 and det (3) = 5, then the value of the det (A2 BC–1) is equal to:

A

65\frac{6}{5}

B

125\frac{12}{5}

C

185\frac{18}{5}

D

245\frac{24}{5}

Answer

125\frac{12}{5}

Explanation

Solution

|A2BC–1| = |A|2 . |B| 1∣C∣\frac{1}{|C|} = 125\frac{12}{5}