text: # Find the inverse of the following matrices by the adjoint method [2-245]. - Mathematics and Statistics
  
  Sum
  
  Find the inverse of the following matrices by the adjoint method [(2, -2),(4, 5)].
  
  #### Solution
  
  Let A = [(2, -2),(4, 5)]
  
  ∴ |A| = [(2, -2),(4, 5)] = 10 + 8 = 18 ≠ 0
  
  ∴ A–1 exists.
  A11 = (– 1)1+1 M11 = (1)(5) = 5
  A12 = (– 1)1+2 M12 = (– 1)(4) = – 4
  A21 = (– 1)2+1 M21 = (– 1)(– 2) = 2
  A22 = (– 1)2+2 M22 = (1)(2) = 2
  ∴  The matrix of the co-factors is
  
  [Aij]2x2 = [("A"_11, "A"_12),("A"_21, "A"_22)] = [(5, -4),(2, 2)]
  
  Now adj A = ["A"_"ij"]_(2xx2)^"T" = [(5, 2),(-4, 2)]
  
  ∴ A–1 = (1)/|"A"|("adj A")
  
  = (1)/(18)[(5, 2),(-4, 2)].
  
  Concept: Inverse of Matrix
  Is there an error in this question or solution?