The sum of all the diagonal elements of a matrix A -

Options :
  1. Is equal to the product of eigen values
  2. is always less than |A|
  3. is always greater than |A|
  4. is equal to the trace of A
Answer and Explanation :-

Answer: Option 4


By definition, Trace of a square matrix = Sum of its diagonal elements = Sum of all its eigen values

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My dear Watson," said [Sherlock Holmes], "I cannot agree with those who rank modesty among the virtues. To the logician all things should be seen exactly as they are, and to underestimate one's self is as much a departure from truth as to exaggerate one's own powers.
-Arthur Conan Doyle The Adventure of the Greek Interpreter