Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Problem
Problem A = [ a b b − a ] A = \begin{bmatrix} a & b \\ b & -a \end{bmatrix} A = [ a b b − a ] M A = A 2 m , m ∈ N , a , b ∈ R MA = A^{2m}, m \in \mathbb{N}, a, b \in \mathbb{R} M A = A 2 m , m ∈ N , a , b ∈ R M M M M = [ a 2 m b 2 m b 2 m − a 2 m ] M = \begin{bmatrix} a^{2m} & b^{2m} \\ b^{2m} & -a^{2m} \end{bmatrix} M = [ a 2 m b 2 m b 2 m − a 2 m ] M = ( a 2 + b 2 ) m [ 1 0 0 1 ] M = (a^2 + b^2)^m \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} M = ( a 2 + b 2 ) m [ 1 0 0 1 ] M = ( a m + b m ) [ 1 0 0 1 ] M = (a^m + b^m) \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} M = ( a m + b m ) [ 1 0 0 1 ] M = ( a 2 + b 2 ) m − 1 [ a b b − a ] M = (a^2 + b^2)^{m-1} \begin{bmatrix} a & b \\ b & -a \end{bmatrix} M = ( a 2 + b 2 ) m − 1 [ a b b − a ] Browse the problem library