Topic: Electronics Engineering
Given that $A=\begin{bmatrix}1&0&0\\ 0&2&0\\ 0&0&3\end{bmatrix}$ Evaluate $A^{3}-6A^{2}+11A-10I$
- A. Null matrix
- B. Identity matrix
- C. -4I
- D. None of these
Answer: C. -4I
Explanation: $A=\begin{bmatrix}1&0&0\\ 0&2&0\\ 0&0&3\end{bmatrix}$, $A^{2}=\begin{bmatrix}1&0&0\\ 0&4&0\\ 0&0&9\end{bmatrix}$, $A^{3}=\begin{bmatrix}1&0&0\\ 0&8&0\\ 0&0&27\end{bmatrix}$
$A^{3}-6A^{2}+11A-10I=\begin{bmatrix}-4&0&0\\ 0&-4&0\\ 0&0&-4\end{bmatrix} = -4\begin{bmatrix}1&0&0\\ 0&1&0\\ 0&0&1\end{bmatrix}=-4I$