32. Find the inverse of the matrix $A=\begin{bmatrix}1 & -1 & 2\\ 0 & 2 & -3\\ 3 & -2 & 4\end{bmatrix}$. Using the inverse, solve the system of linear equations $x-y+2z=1; 2y-3z=1; 3x-2y+4z=3$.

(i) Form the equations required to solve the problem of finding the price of each item, and express it in the matrix form $AX = B$. (ii) Find $|A|$ and confirm if it is possible to find $A^{-1}$. (iii) (a) Find $A^{-1}$, if possible, and write the formula to find $X$. OR (iii) (b) Find $A^2 - 8I$, where $I$ is an identity matrix.

If $A\cdot(\text{adj }A)=\begin{bmatrix}3&0&0\\ 0&3&0\\ 0&0&3\end{bmatrix}$, then the value of $|A|+| \text{adj }A|$ is equal to :

If $A=\begin{bmatrix}1 & 2 & 3\\ 3 & -2 & 1\\ 4 & 2 & 1\end{bmatrix}$, then show that A³ - 23A - 40I = O.

\(If~A=\begin{bmatrix}-2&0&0\\ 1&2&3\\ 5&1&-1\end{bmatrix},\) then the value of | A (adj. A) | is: