Question

If $A= \begin{bmatrix} 1 & 0 & 0 \\\ x & 1 & 0 \\\ x & x & 1 \\\ \end{bmatrix}$ and $I= \begin{bmatrix} 1 & 0 & 0 \\\ 0 & 1 & 0 \\\ 0 & 0 & 1 \\\ \end{bmatrix} ,$ then ${{A}^{3}}-4{{A}^{2}}+3A+I$ is equal to

• A. $3I$
• B. $I$
• C. $-I$
• D. $-2I$

Answer 1

Answer: (B)

$I$

Answer 2

Given, $A=\left| \begin{matrix} 1 & 0 & 0 \\\ x & 1 & 0 \\\ x & x & 1 \\\ \end{matrix} \right|\Rightarrow A=1$
$\therefore$ ${{A}^{3}}-4{{A}^{2}}+3A+I={{(1)}^{3}}-4{{(1)}^{3}}+3(1)+I$
$=I$