. Let A = 
= 
adj. A = 
A. (adj. A) = 
= 
= 
……….(i)
Again (adj. A). A =
= 
= ……….(ii)
And
= 
Also 
= ……….(iii)
From eq. (i), (ii) and (iii) A. (adj. A) = (adj. A). A = 
Verify $A(\operatorname{adj} \mathbf{A})=(\operatorname{adj} \mathbf{A}) \mathbf{A}=|\mathbf{A}| \mathbf{I}$ in $\left[\begin{array}{ccc}1 & -1 & 2 \\ 3 & 0 & -2 \\ 1 & 0 & 3\end{array}\right]$
Verify $A(\operatorname{adj} \mathbf{A})=(\operatorname{adj} \mathbf{A}) \mathbf{A}=|\mathbf{A}| \mathbf{I}$ in $\left[\begin{array}{ccc}1 & -1 & 2 \\ 3 & 0 & -2 \\ 1 & 0 & 3\end{array}\right]$