1 votes 1 votes Let A be n*n matrix,$A^{n}$ = $A^{n-1}$ for n>=1 and $A^{0}$=I,Which of following is true? a.$A^{m}$ .$A^{n}$ =$A^{m+n}$ b. $($A^{m}$)^{n}$=$A^{mn}$$ c. both a and b c none Linear Algebra engineering-mathematics linear-algebra + – rahul sharma 5 asked Jun 25, 2017 rahul sharma 5 340 views answer comment Share Follow See all 5 Comments See all 5 5 Comments reply rahul sharma 5 commented Jun 25, 2017 reply Follow Share Second option is (A^m)^n. It is showing correct in preview but not in question. my doubt here is do i need to check that whether matrix is singular or not here. As i know that power of groups are can be written like in option a and b.But there it is not given it is singular matrix.So do we need to check for group first ,here? If yes,then which statement is implying in above that it is non singular matrix? 0 votes 0 votes erh commented Jun 26, 2017 reply Follow Share answer is c? $A^{n} = A^{n-1}$ n>=1 and $A^{0} = I$ , i think this is sufficient to tell that A is not singular matrix, put n=1 this implies $A^{1} = A^{0}= I$ and similarly $A^{k}........A^{4} = A^{3}=A^{2} = A^{1}= I$ $k \epsilon Z$ i think that makes both a and b statements are correct 0 votes 0 votes rahul sharma 5 commented Jun 26, 2017 reply Follow Share Can you please tell again how are you saying this is non singular? 0 votes 0 votes erh commented Jun 26, 2017 reply Follow Share because I is non singular 0 votes 0 votes rahul sharma 5 commented Jun 26, 2017 reply Follow Share But what about other matrices ?How can i be sure that the set of these matrices is non singular? 0 votes 0 votes Please log in or register to add a comment.