If a matrix A= [ array ll 1 & 1 1 & 1 array ] satisfies A^6=k A^ , then the value of k is

Step-by-step solution

A= [ array ll 1 & 1 1 & 1 array ] aligned & A^2= [ array ll 1 & 1 1 & 1 array ] [ array ll 1 & 1 1 & 1 array ]= [ array ll 2 & 2 2 & 2 array ] & A^3= [ array ll 2 & 2 2 & 2 array ] [ array ll 1 & 1 1 & 1 array ]= [ array ll 4 & 4 4 & 4 array ]= [ array ll 2^2 & 2^2 2^2 & 2^2 array ] & A^4= [ array ll 8 & 8 8 & 8 array ]= [ array ll 2^3 & 2^3 2^3 & 2^3 array ] & A^6= [ array ll 2^5 & 2^5 2^5 & 2^5 array ]=2^5 [ array ll 1 & 1 1 & 1 array ] 2^5=32 & k =32 aligned