Let A = [ array cc 1 & 2 -1 & 4 array ] and A ⁻¹= I + A , , R , I is the identity matrix of order 2 , then 4( - ) is

Step-by-step solution

|A|= | array cc 1 & 2 -1 & 4 array |=4+2=6 0 If A= [ array ll a & b c & d array ] and ad - bc 0 , then aligned A⁻¹ & = 1 a d-b c [ array cc d & -b -c & a array ] A⁻¹ & = 1 6 [ array cc 4 & -2 1 & 1 array ] . aligned aligned & A⁻¹= I+ A & 1 6 [ array cc 4 & -2 1 & 1 array ]= [ array cc & 0 0 & array ]+ [ array cc & 2 - & 4 array ] & [ array cc 2 3 & - 1 3 1 6 & 1 6 array ]= [ array cc + & 2 - & +4 array ] aligned By the equality of matrices, aligned & 1 6 =- and + = 2 3 & = -1 6 and - 1 6 = 2 3 & = -1 6 and = 5 6 &