If A⁻¹= -1 2 [ array cc 5 & 8 -1 & 2 array ] , then 2 A+I₂= , where I₂ is a unit matrix of order 2

Step-by-step solution

aligned & A ⁻¹= -1 2 [ array cc 1 & -4 -1 & 2 array ]= [ array cc -1 2 & 2 1 2 & -1 array ] & AA ⁻¹= I A [ array cc -1 2 & 2 1 2 & -1 array ]= [ array ll 1 & 0 0 & 1 array ] aligned aligned & R ₂ R ₁+ R ₂ & ~A [ array ll -1 2 & 2 0 & 1 array ]= [ array ll 1 & 0 1 & 1 array ] & R ₁ R ₁+2 R ₂ & ~A [ array cc -1 2 & 0 0 & 1 array ]= [ array cc -1 & -2 1 & 1 array ] & R ₁ -2 R ₁ & ~A [ array ll 1 & 0 0 & 1 array ]= [ array ll 2 & 4 1 & 1 array ] A = [ array ll 2 & 4 1 & 1 array ] & 2 ~A + I ₂= [ array ll 4 & 8 2 & 2 ar