Let A be a 2 2 symmetric matrix such that A [ array l 1 1 array ]= [ array l 3 7 array ] and the determinant of A be 1 . If A⁻¹= A+ I , where I is an identity matrix of order 2 2 , then + equals _______

Step-by-step solution

aligned & Let A= [ array ll a & b b & d array ] & [ array ll a & b b & d array ] [ array l 1 1 array ]= [ array l 3 7 array ], a d-b^2=1 & a+b=3, b+d=7,(3-b)(7-b)-b^2=1 & 21-10 b=1 b=2, a=1, d=5 & A= [ array ll 1 & 2 2 & 5 array ], A⁻¹= [ array cc 5 & -2 -2 & 1 array ] & A⁻¹= A+ I & [ array cc 5 & -2 -2 & 1 array ]= [ array cc + & 2 2 & 5 + array ] & =-1, =6 + =5 aligned