UPSC NDA I and II 2020 Math Solved Paper

A square M matrix is said to be Hermitian (or self-adjoint) if it is equal to its. Own Hermitian conjugate, i.e. (M)T=M
Given Matrix A=[

1−i	i
−i	1−i

]
(A)T=[

1+i	i
−i	1+i

]
Now, A+(A)T =[

1−i	i
−i	1−i

]+[

1+i	i
−i	1+i

] =[

2	2i
−2i	2

] =2[

1	i
−i	1

]
Conjugate transpose of (A+(A)T)=2[

1	i
−i	1

]
Hence, (A)T+A is hermitian