If A⁻¹= [ array lll 3 & 2 & 6 1 & 1 & 2 2 & 5 & 5 array ] , then A=

Step-by-step solution

Let A ⁻¹ ~A = I aligned & [ array lll 3 & 2 & 6 1 & 1 & 2 2 & 5 & 5 array ] A= [ array ccc 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ] & R₂ 3 R₂-R₁ and R₃ 3 R₃-2 R₁ & [ array ccc 3 & 2 & 6 0 & 1 & 0 0 & 11 & 3 array ] A= [ array ccc 1 & 0 & 0 -1 & 3 & 0 -2 & 0 & 3 array ] & R₁ R₁-2 R₂ and R₃ R₃-11 R₂ aligned aligned & [ array lll 3 & 0 & 6 0 & 1 & 0 0 & 0 & 3 array ] A= [ array ccc 3 & - & 0 -1 & 3 & 0 9 & -33 & 3 array ] & R ₁ R ₁-2 R ₃ & [ array lll 3 & 0 & 0 0 & 1 & 0 0 & 0 & 3 array ] A = [ array ccc -15 & 60 & -6 -1