If A= [ array ll 1 & a 0 & 1 array ] where a N , then what is A¹⁰⁰-A⁵⁰-2 A²⁵ equal to? where I is the identity matrix.

Step-by-step solution

aligned & A= [ array ll 1 & a 0 & 1 array ] A^2= [ array cc 1 & 2 a 0 & 1 array ] A^3= [ array cc 1 & 3 a 0 & 1 array ] & A^n= [ array cc 1 & n a 0 & 1 array ] aligned aligned & Now, A¹⁰⁰-A⁵⁰-2 A²⁵ & = [ array cc 1 & 100 a 0 & 1 array ]- [ array cc 1 & 50 a 0 & 1 array ]-2 [ array cc 1 & 25 a 0 & 1 array ] & = [ array cc -2 & 0 0 & -2 array ]=-2 I . aligned