Let A= [ array cc 2 & -1 0 & 2 array ] . If B = I - ^3 C ₁( adj A )+ ^3 C ₂( adj A )^2- ^3 C ₃( adj A )^3 , then the sum of all elements of the matrix B is

Step-by-step solution

aligned B & = I - ^3 C ₁( adj A )+ ^3 C ₂( adj A )^2- ^3 C ₃( adj A )^3 & = I -3 adj A +3( adj A )^2-1( adj A )^3 & =( I - adj A )^3 adj A & = [ array ll 2 & 1 0 & 2 array ] B & = ( [ array ll 1 & 0 0 & 1 array ]- [ array ll 2 & 1 0 & 2 array ] )^3 & = [ array rr -1 & -1 0 & -1 array ] & = [ array rr -1 & -1 0 & -1 array ] [ array rr -1 & -1 0 & -1 array ] [ array cc -1 & -1 0 & -1 array ] & = [ array rr 1 & 2 0 & 1 array ] [ array rr -1 & -1 0 & -1 array ] & = [ array rr -1 & -3 0 & -1 array ] aligned Sum of all e