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Q.

Using the elements -3,-2,-1, 0,1,2,3, and then which are following are false 

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a

The number of  3X3 matrices are 729

b

The number of 3X3 skew symmetric matrices are 74

c

The number of 3X3 matrices having trace 0 are is 3776

d

The number of 3X3  scalar matrices are 6

answer is A, B, D.

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Detailed Solution

1) number of 3x3 matrices  =79
2) number of 3x3 Skew symmetric matrices  =73
 3) Trace is zero 
  diatonal elements  1,2,31,2,31,1,21,1,2     0,0,01,1,02,2,03,3,0}37
Remaining elements = 76
4) all diagonal elements are equal and remaining are zero
Then number of scalar matrices=7
 

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