Let A= [ array cc 2 & -1 1 & 1 array ] . If the sum of the diagonal elements of A¹³ is 3^n , then n is equal to_________

Step-by-step solution

A= [ array cc 2 & -1 1 & 1 array ] aligned & A^2= [ array cc 2 & -1 1 & 1 array ] [ array cc 2 & -1 1 & 1 array ]= [ array cc 3 & -3 3 & 0 array ] & A^3= [ array cc 3 & -3 3 & 0 array ] [ array cc 2 & -1 1 & 1 array ]= [ array cc 3 & -6 6 & -3 array ] & A^4= [ array cc 3 & -6 6 & -3 array ] [ array cc 2 & -1 1 & 1 array ]= [ array cc 0 & -9 9 & -9 array ] & A^5= [ array cc 0 & -9 9 & -9 array ] [ array cc 2 & -1 1 & 1 array ]= [ array cc -9 & -9 9 & -18 array ] & A^6= [ array cc -9 & -9 9 & -18 array ] [ array cc 2