GEEKS 4 GEEKS - gate cs mock 2018

Question

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

• A. 7/4
• B. 1/7
• C. 7
• D. 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?

Comments

Orthogonal matrix means $AA^T=I$

So, $A^T=\frac{I}{A}$

The eigen values of $A^T$ are inverse of A's.

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But trace should not change as diagonal elements of $A^T$  would be the same as A

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Oh yes.. you are right..

The question is wrong..

Orthogonal matrix can have eigen values whose magnitude is 1. Eg: +1,-1,1/2+i/2