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Q.

If A is a diagonal matrix of order 3 x 3 is commutative with every square matrix of order 3 x 3 under multiplication and tr(A) = 12, then the value of A is ______________.

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answer is 64.

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Detailed Solution

A diagonal matrix is commutative with every square matrix if it is scalar matrix; so every diagonal element is 4. Therefore, |A| = 64.

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