Let A= [ array ll 3 & -4 1 & -1 array ] and B be two matrices such that A¹⁰⁰=100 B+I . Then the sum of all the elements of B ¹⁰⁰ is _ _ _ _

Step-by-step solution

A = I + bmatrix 2 & -4 1 & -2 bmatrix , let M = bmatrix 2 & -4 1 & -2 bmatrix M^2 = bmatrix 0 & 0 0 & 0 bmatrix = M^3 = M^4 = = M¹⁰⁰ A¹⁰⁰ = (I + M)¹⁰⁰ = _ r=0 ¹⁰⁰ 100 r M^r I A¹⁰⁰ = I + 100M = I + 100B M = B M¹⁰⁰ = B¹⁰⁰ = bmatrix 0 & 0 0 & 0 bmatrix