• # question_answer If the matrix $\left[ \begin{matrix} 1 & 2a & 2 \\ 0 & -1 & 1 \\ a & 1 & 3 \\ \end{matrix} \right]$ is not equivalent to ${{I}_{3}}$ then a is, $a\in R.$ A) 1 B) 2 C) 4 D) No such 'a' exists

 $A\,3\times 3$ matrix is equivalent to ${{I}_{3}}$ if it is non-singular. Hence $\left| \begin{matrix} 1 & 2a & 2 \\ 0 & -1 & 1 \\ a & 1 & 3 \\ \end{matrix} \right|\,\,=0$$\Rightarrow$ $-\,4+a\,(2a+2)=0$$\Rightarrow$$2{{a}^{2}}+2a-4=0$$\Rightarrow$            $(a+2)\,\,(a-1)=0\to a=-\,2,\,\,1$