Mathematics

Problem

Let

A=\begin{pmatrix}1 & 0 & 2\\2 & -1 & 3\\3 & 4 & 1\end{pmatrix}.

(i) Evaluate

|A|

. (ii) Form the cofactor matrix of

A

and hence obtain

\operatorname{adj}A

. (iii) Determine

A^{-1}

. (iv) Verify that

AA^{-1}=I_3