Question

If $A=\left[\begin{array}{cc}4& x+2\\ 2x-3& x+1\end{array}\right]$ is an invertible matrix, then $x$ cannot take value

• A. -1
• B. 2
• C. 3
• D. none of these

Answer 1

The correct option is D none of these

$\text{det}\left(A\right)=\left|\begin{array}{cc}4& x+2\\ 2x-3& x+1\end{array}\right|=4(x+1)-(x+2)(2x-3)$
$=4x+4-(2x^2+4x-3x-6)=10+3x-2x^2$
Now for A to be invertible, $\text{det}\left(A\right)\ne 0$
Clearly at $x=-1,2,3$ $\text{det}\left(A\right)\ne 0$
Hence option D is correct choice.