Consider the following in respect of the matrix A = ( array cc -1 & 1 1 & -1 array ) 1. A ^2=- A 2. A ^3=4 ~A Which of the above is/are correct?

Step-by-step solution

aligned & A= [ array cc -1 & 1 1 & -1 array ] & A A= [ array cc -1 & 1 1 & -1 array ] [ array cc -1 & 1 1 & -1 array ] & = [ array cc 2 & -2 -2 & 2 array ]=-2 [ array cc -1 & 1 1 & -1 array ] & A^2=-2 A & A^2 A=-2 [ array cc -1 & 1 1 & -1 array ] [ array cc -1 & 1 1 & -1 array ] & =-2 [ array cc 2 & -2 -2 & 2 array ]=4 [ array cc -1 & 1 1 & -1 array ] & A^3=4 A aligned Hence A^2 -A, A^3=4 A