The matrix {bmatrix}0 & -4+i \\ 4+i & 0{bmatrix} is [NDA I 2015]

Correct Answer is : Skew-Hermitian

Correct Answer is : Skew-Hermitian

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UPSC NDA I 2015 Mathematics Solved Paper

Question : 8 of 120

Marks: +1, -0

The matrix

\begin{bmatrix}0 & -4+i \\ 4+i & 0\end{bmatrix}

Solution:

For a Hermitian matrix

A = A^{\overline{T}}

Given that the elements of the matrix are complex numbers.

Then it is Skew-Hermitian matrix

Applying the above concepts to the given question, we get

A=\begin{pmatrix}0 & -4+i \\ 4+i & 0\end{pmatrix}

A^T=\begin{pmatrix}0 & 4+i \\ -4+i & 0\end{pmatrix}

A^{\overline{T}}=\begin{pmatrix}0 & 4-i \\ -4-i & 0\end{pmatrix}

=\begin{pmatrix}0 & -(-4+i) \\ -(4+i) & 0\end{pmatrix}

=-\begin{pmatrix}0 & -4+i \\ 4+i & 0\end{pmatrix}

=-A

Therefore, the above matrix is skew-Hermitian matrix.

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