If $$A=x$$−yy−zz−xy−zz−xx−yz−xx−yy−z ,then trace of A is

Operations of matrix

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Question

If $A = [\begin{array}{ccc} x - y & y - z & z - x \\ y - z & z - x & x - y \\ z - x & x - y & y - z \end{array}]$ ,then trace of A is

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Solution

$t r a c e o f A = s u m o f t h e p r i n c i p a l d i a g o n a l e l e m e n t s = (x - y) + (z - x) + (y - z) = 0$

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