Given 2A∗+B∗=[−2i−4i−6i−8i] and all the elements of B are 2. Then matrix A is given by. (∗ represents transpose conjugate operator)
[−1+i−1+2i−1+3i−1+4i]
Given that 2A∗+B∗=[−2i−4i−6i−8i] and B=[2222]
Then 2A∗+2[1111]=[−2i−4i−6i−8i]
( SInce elements of B are all same and is equal to a real number →B∗=B )
A∗=[−2i−1−2i−1−3i−1−4i−1]A=∴(A∗)∗=[i−13i−12i−14i−1]
(This is a property. If conjugate transpose is done twice on a matrix you will get the original matrix)
Hence the option (b)