Define Adjoint of a Matrix

Adjoint of a Matrix

If A is a square matrix then the transpose of a matrix obtained by replacing the elements of A by their co-factors is called the adjoint of a matrix A and is denoted by Adj A. For example,

Adjoint of a Matrix

Note

  1. Adjoint-of-identity-and-null-matrix
  2. If A is a square matrix of order ‘3’ and K is any scalar then Adj (KA) = K^2 Adj A
    Proof :-
    Adjoint-of-KA-matrix

    Likewise, If A is square matrix of order ‘n’ then Adjoint of KA = K to the power of (n-1) times Adjoint of A

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