1 votes 1 votes Given an orthogonal matrix $A,$ $(AA^{T})^{-1}$ is _______ $2I$ $I$ $I/2$ $A$ Linear Algebra go2025-mix-4 matrix + – gatecse asked Nov 27, 2020 • edited Nov 28, 2020 by Lakshman Bhaiya gatecse 76 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes A matrix $A$ is orthogonal if its transpose is equal to its inverse $:A^{T} = A^{-1}$ $\implies AA^{T} = AA^{-1} = I$ Then $(AA^{T})^{-1} = I^{-1} = I.$ So, the correct answer is $(B).$ gatecse answered Nov 27, 2020 gatecse comment Share Follow See all 0 reply Please log in or register to add a comment.