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If A is a diagonal matrix of order 3xx3 ...

If A is a diagonal matrix of order `3xx3` is commutative with every square matrix of order `3xx3` under multiplication and trace (A)=12, then find |A|

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The correct Answer is:
64
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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CENGAGE ENGLISH-MATRICES-Numerical Value Type
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  2. Let A=[a("ij")](3xx3) be a matrix such that A A^(T)=4I and a("ij")+2c(...

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  3. Let S be the set which contains all possible vaues fo I ,m ,n ,p ,q ,r...

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  4. If A is a diagonal matrix of order 3xx3 is commutative with every squa...

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  5. If A is a square matrix of order 3 such that |A|=2,t h e n|(a d jA^(-1...

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  6. If A and B are two matrices of order 3 such that AB=O and A^(2)+B=I, t...

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  7. If a, b, and c are integers, then number of matrices A=[(a,b,c),(b,c,a...

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  8. Let A=[a("ij")] be 3xx3 matrix and B=[b("ij")] be 3xx3 matrix such tha...

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  9. A square matrix M of order 3 satisfies M^(2)=I-M, where I is an identi...

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  10. Let A=[a("ij")](3xx3), B=[b("ij")](3xx3) and C=[c("ij")](3xx3) be any ...

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  11. If A is a square matrix of order 2xx2 such that |A|=27, then sum of th...

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  12. If A is a aquare matrix of order 2 and det. A=10, then ((tr. A)^(2)-tr...

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  13. Let A and B are two square matrices of order 3 such that det. (A)=3 an...

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  14. Let P, Q and R be invertible matrices of order 3 such A=PQ^(-1), B=QR^...

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  15. If A=[(1,x,3),(1,3,3),(2,4,4)] is the adjoint of a 3xx3 matrix B and d...

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  16. A, B and C are three square matrices of order 3 such that A= diag (x, ...

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  17. Let A=[a("ij")] be a matrix of order 2 where a("ij") in {-1, 0, 1} and...

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  18. Let K be a positive real number and A=[2k-1 2sqrt(k)2sqrt(k)2sqrt(k)1-...

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  19. Let M be a 3xx3 matrix satisfying M[0 1 0]=[-1 2 3] ,M[1-1 0]=[1 1-1],...

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  20. let z= (-1+sqrt(3i))/2, where i=sqrt(-1) and r,s epsilon P1,2,3}. Let ...

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