Before studying this chapter, you will need to have a deep knowledge about:
Adjoint of Matrix
Let $\text{A = } [ a_{ij} ]_\text{mxn}$ be a matrix whose respective co-factors are $\text{C}_\text{ij}$. Then, the tranpose of co-factor matrix of a given matrix is defined as adjoint Matrix.
Mathematically,
Adjoint of matrix = $[ \text{C}_\text{ji} ]$
Adjoint of a 2×2 Matrix
Let $\text{A} \ = \left ( \displaylines{ a & b \\ c & d} \right )_\text{2×2}$ be a 2×2 matrix then the adjoint of matrix A is defined as
Adjoint of A = $\left ( \displaylines{ d & – b \\ -c & a} \right)_\text{2×2}$
Adjoint of a 3×3 Matrix
Let $\text{A} = \left ( \displaylines{a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}} \right )_{3\text{x}3}$ be a 3×3 matrix then, the adjoint of A is defined as
Adjoint of A = $\left ( \displaylines{C_{11} & C_{21} & C_{31} \\ C_{12} & C_{22} & C_{32} \\ C_{13} & C_{23} & C_{33}} \right )_{3\text{x}3}$
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