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GEEKS 4 GEEKS - gate cs mock 2018

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An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix A^T?

  1. 7/4
  2. 1/7
  3. 7
  4. 4/7

Answer given : 7/4

My answer : 7

trace of a matrix is the sum of its diagonal elements.So on transposing the matrix the diagonal elements will remain same and hence it's trace should not change.

So trace of transpose(A) = trace of A

And trace is also equal to sum of eigen values.So trace of A = 7

So trace of transpose(A) should be 7.

Is my reasoning right?

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