IGNOU MTE 2 2026 - Find the values of for which the matrix

Question

Find the values of $a, b \in \mathbf{C}$ for which the matrix

$$\begin{bmatrix} 1 & i & 1+i \\ a & 0 & b \\ 1-i & 2+i & 1 \end{bmatrix}$

is Hermitian.

09 Jan 2026

Answer :

Word Count : 150

For a matrix to be Hermitian, it must be equal to its conjugate transpose, so each diagonal entry must be real and each off-diagonal entry must be the complex conjugate of the corresponding symmetric entry. The diagonal entries are 1, 0, and 1, all of which are real, so no condition arises from the diagonal. Comparing the (1,2) and

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