if for a matrix A , A to the power 5 = I , THEN A inverse = Share with your friends Share 0 Himanshu answered this 2 View Full Answer Swoyamsiddha Behera answered this A^{2} is A therefore A^{5} can be written as A^{2}.A^{2}.A which gives us A.A.A which can be further written as A^{2}.A = A.A and it is equal to A now A=I multiplying both sides by A^{-1} we get A.A^{-1} = I.A^{-1} implies A^{-1 }= A^{-1}/A 2