Maths · Matrices, algebra of matrices, type of matrices
If , \) then is equal to
If \( \boldsymbol{A}=\left[\begin{array}{cc}-\boldsymbol{i} & \mathbf{0} \\ \mathbf{0} & \boldsymbol{i}\end{array}\right], \) then \( \boldsymbol{A}^{\prime} \boldsymbol{A} \) is equal to
- A. \( I \)
- B. \( -i A \)
- C. -I \)
- D. \( i A \)
Step-by-step solution
Given A = [[-i, 0], [0, i]], its conjugate transpose A' = [[i, 0], [0, -i]]. Then A'A = [[i,0],[0,-i]] * [[-i,0],[0,i]] = [[i*(-i), 0], [0, (-i)*i]] = [[-i^2, 0], [0, -i^2]] = [[1,0],[0,1]] = I.
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