If A is a diagonal matrix of order 3X3 is commutative with every square matrix of order 3x3 under multiplication and tr(A) =12, then the value of |A| is :

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Please find below the solution to the asked query:

Any 3×3 Diagonal matrix which commutes with all other 3×3 square matricesis given by:A=x000x000xTrace=Sum of diagonal entries=12a+a+a=123a=12a=4A=400040004Expand along R1A=44×4-0=4×16=64 Answer

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