0 votes 0 votes In this question – https://gateoverflow.in/348646/Gate-overflow-linear-algebra-1-10 for $A=\begin{bmatrix} 0 & i\\ -i& 0 \end{bmatrix}$ how is (B) valid ? Linear Algebra test-series gateoverflow linear-algebra engineering-mathematics + – o asked Jan 31, 2022 • edited Jan 31, 2022 by o o 519 views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply palashbehra5 commented Jan 31, 2022 reply Follow Share https://en.m.wikipedia.org/wiki/Skew-symmetric_matrix#Properties Yep, the matrix needs to be real as well. 1 votes 1 votes o commented Jan 31, 2022 reply Follow Share ok thanks a lot in the exam, if nothing is specified we can take an imaginary matrix for counter-example, right? 0 votes 0 votes palashbehra5 commented Jan 31, 2022 reply Follow Share yep, that would work. 1 votes 1 votes Kabir5454 commented Jan 31, 2022 reply Follow Share option should be “When the identity matrix is added to a real skew-symmetric matrix, the resultant matrix is invertible.” 1 votes 1 votes Please log in or register to add a comment.