0 votes 0 votes If a, b are elements of a group G, then (ba)-1 = Discrete Mathematics group-theory + – hem chandra joshi asked Nov 5, 2017 hem chandra joshi 316 views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply Anu007 commented Nov 5, 2017 reply Follow Share (ba)-1 = a-1 *b-1 0 votes 0 votes hem chandra joshi commented Nov 5, 2017 reply Follow Share proof? 0 votes 0 votes santhoshdevulapally commented Nov 5, 2017 reply Follow Share Matrix multiplication is a group only if two matrices 'a' and 'b' are non singular. Consider two non singular matrices 'a' and 'b' and perform ba(multiplication) and inverse of the matrix. same as $b^{-1}*a^{-1}$. If these two are same then it satisfies the above properety. 0 votes 0 votes akash.dinkar12 commented Nov 5, 2017 reply Follow Share we should know 2 facts before proving it: 1. Inverse is applicable only for square matrices. 2.Let X be any n*n square matrix, then a matrix Y if it exists such that XY=YX=In-------((Identity matrix of size n*n) If this condition is true then we can say Both X and Y are inverses of each other. X-1 =Y or Y-1 = X To prove : (ba)-1 = a-1b-1 Assume X =(ba)-1 Y=a-1b-1 My aim will be XY=YX=In XY= (ba)(a-1 b-1 ) =baa-1b-1 =In YX= (a-1 b-1 )(ba) =a-1b-1 ba =In 1 votes 1 votes Please log in or register to add a comment.