If A= [ array cc 1 & 2 -5 & 1 array ] and A⁻¹=x A+y I , where I is unit matrix of order 2 , then the values of x and y are respectively

Step-by-step solution

| A |= | array cc 1 & 2 -5 & 1 array |=1+10=11 and adj A = [ array cc 1 & -2 5 & 1 array ] A ⁻¹= 1 11 [ array cc 1 & -2 5 & 1 array ] Given A ⁻¹= x A + yI 1 11 [ array cc 1 & -2 5 & 1 array ]= [ array cc x & 2 x -5 x & x array ]+ [ array ll y & 0 0 & y array ] 1 11 [ array cc 1 & -2 5 & 1 array ] = [ array cc x + y & 2 x -5 x & x + y array ] 2 x = -2 11 x = -1 11 and x + y = 1 11 y = 2 11