Let A= [ array cc & -1 6 & array ], 0 , such that det (A)=0 and + =1 . If I denotes 2 2 identity matrix, then the matrix (1+ A )^8 is:

Step-by-step solution

aligned & | A |=0 & +6=0 & =-6 & + =1 & =3, =-2 & ~A = [ array ll 3 & -1 6 & -2 array ] & A ^2= [ array ll 3 & -1 6 & -2 array ] [ array ll 3 & -1 6 & -2 array ]= [ array ll 3 & -1 6 & -2 array ] & A ^2= A & A = A ^2= A ^3= A ^4= A ^5 & ( I + A )^8 & = I + ^8 C ₁ ~A ^7+ ^8 C ₂ ~A ^6+ . .+ ^8 C ₈ ~A ^8 & = I + A ( ^8 C ₁+ ^8 C ₂+ . .+ ^8 C ₈ ) & = I + A (2^8-1 ) & = [ array ll 1 & 0 0 & 1 array ]+ [ array cc 765 & -255 1530 & -510 array ] aligned = [ array cc 766 & -255 1530 & -509 array ]