If A= [ array ccc -1 & 1 & 2 1 & 2 & 3 3 & 1 & 1 array ] then the inverse of (A I)^t (where I is an identity matrix) is

Step-by-step solution

Since AI = A , we need (A^t)⁻¹ . A^t = bmatrix -1 & 1 & 3 1 & 2 & 1 2 & 3 & 1 bmatrix |A^t| = -1(2-3) - 1(1-2) + 3(3-4) = 1 + 1 - 3 = -1 Cofactors of A^t : C₁₁ = -1, C₁₂ = 1, C₁₃ = -1 C₂₁ = 8, C₂₂ = -7, C₂₃ = 5 C₃₁ = -5, C₃₂ = 4, C₃₃ = -3 adj (A^t) = C^t = bmatrix -1 & 8 & -5 1 & -7 & 4 -1 & 5 & -3 bmatrix (A^t)⁻¹ = 1 -1 bmatrix -1 & 8 & -5 1 & -7 & 4 -1 & 5 & -3 bmatrix = bmatrix 1 & -8 & 5 -1 & 7 & -4 1 & -5 & 3 bmatrix