1 votes 1 votes If A=$\begin{bmatrix} 1 & 2\\ -1& 3 \end{bmatrix}$ then $\ A^{6} -4A^{5}+8A^{4}-12A^{3}+14A^{2}$=? a)0 b)4A c)4A+5I d)-4A+5I am gettind d Gate Fever asked Jan 3, 2019 Gate Fever 530 views answer comment Share Follow See all 8 Comments See all 8 8 Comments reply ank73811 commented Jan 3, 2019 i edited by ank73811 Jan 3, 2019 reply Follow Share I am getting the answer as (-A^2) = 5I - 4A 0 votes 0 votes Gate Fever commented Jan 3, 2019 reply Follow Share A^2= 4A-5I PLS CHECK AGAIN 1 votes 1 votes Lakshman Bhaiya commented Jan 3, 2019 reply Follow Share I got $A^{2}=4A-5I$ 0 votes 0 votes Gate Fever commented Jan 3, 2019 reply Follow Share @Lakshman Patel RJIT whats the final answer shouldn't it be d?? 0 votes 0 votes Lakshman Bhaiya commented Jan 3, 2019 reply Follow Share @Gate Fever $A^{2}=4A-5I$ $A^{3}=11A-20I$ $A^{4}=24A-55I$ $A^{5}=41A-120I$ $A^{6}=44A-205I$ Try to substitute the value of the above equation ,you will get the answer is $-4A+5I$ 1 votes 1 votes Gate Fever commented Jan 3, 2019 reply Follow Share thats what i am saying that option d is correct!! they have given wrong answer!! 0 votes 0 votes ank73811 commented Jan 3, 2019 reply Follow Share You can make use of characteristic equation to simplify the problem which is A^2 - 4A + 5I = 0 0 votes 0 votes Lakshman Bhaiya commented Jan 3, 2019 reply Follow Share @Gate Fever Yes you are right. 0 votes 0 votes Please log in or register to add a comment.