Question

If ${\displaystyle A=\left[\begin{array}{cc}2& -3\\ 3& 5\end{array}\right]}$ then find A^-1 by adjoint method. 

Answer 1

Given ${\displaystyle A=\left[\begin{array}{cc}2& -3\\ 3& 5\end{array}\right]}$

${\displaystyle \therefore \left|A\right|=\left|\begin{array}{cc}2& -3\\ 3& 5\end{array}\right|=10+9=19\ne 0}$

∴A^-1 exist

A₁₁ = (-1)¹⁺¹.M₁₁ = 5

A₁₂ = (-1)¹⁺².M₁₂ = -3

A₂₁ = (-1)²⁺¹.M₂₁ = -(-3) = 3

A₂₂ = (-1)²⁺².M₂₂ = 2

Hence, matrix of the co-factors is