If A= [ array ll 1 & 0 1 & 1 array ] and A⁸=a A+b I , then (a, b)=

Step-by-step solution

We have, A= [ array ll 1 & 0 1 & 1 array ]A²=A A= [ array ll 1 & 0 1 & 1 array ] [ array ll 1 & 0 1 & 1 array ]= [ array ll 1 & 0 2 & 1 array ]A³=A² A= [ array ll 1 & 0 2 & 1 array ] [ array ll 1 & 0 1 & 1 array ]= [ array ll 1 & 0 3 & 1 array ] Similarly, A⁸= [ array ll 1 & 0 8 & 1 array ] Now, A⁸=a A+b I aligned & [ array ll 1 & 0 8 & 1 array ]=a [ array ll 1 & 0 1 & 1 array ]+b [ array ll 1 & 0 0 & 1 array ] & [ array ll 1 & 0 8 & 1 array ]= [ array cc a+b & 0 a & a+b array ] & a=8 and a+b=1 & b=1-8=-7 aligned