1. Determinant of a matrix 1x1 order A = [a₁₁]1×1 is given by |a₁₁| = a₁₁
2. Determinant of a matrix 2x2 order 
3. Determinant of a matrix 3x3 order 
   
    

1. The area of a triangle whose vertices are (x₁, y₁), (x₂, y₂) and (x₃, y₃), is given by the expression 
   Area of triangle = 1/2[x₁(y₂–y₃) + x₂ (y₃–y₁) + x₃ (y₁–y₂)]. 
    
    

1. The adjoint of a square matrix A = [aᵢⱼ]n × n is defined as the transpose of the matrix [Aᵢⱼ]n × n,
   where Aᵢⱼ is the cofactor of the element aᵢⱼ. Adjoint of the matrix A is denoted by adj A.
2. Inverse of matrix A, A-1 = 1/|A| x adj(A)
    

    
1. AX = B or A-1 
  (AX) = A-1B (premultiplying by A-1) or 
  (A-1A) X = A-1B (by associative property) or 
  IX = A-1B or 
  X = A-1B