1 votes 1 votes A be a n-square matrix with integer entries and B = A + 12 I. Then (a) B is idempotent (b) B inverse exist (c) B is nilpotent (d) B inverse is idempotent Linear Algebra linear-algebra matrix + – learncp asked Aug 25, 2015 learncp 2.0k views answer comment Share Follow See 1 comment See all 1 1 comment reply lolster commented May 29, 2019 reply Follow Share What if A = -12 I? Then, B inverse doesn't exist. Also, in this case, A is an n-square matrix with integer entries. Hence this assumption for A is valid. 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes answer is (c) let a=[1 2 3 4] then B^2 will not be B hence not idempotent, B^2 is not 0 so not nilpotent but as B is a square matrix so we can find inverse. cse23 answered Aug 25, 2015 cse23 comment Share Follow See all 0 reply Please log in or register to add a comment.