$A =\begin{bmatrix}1/3&2\\0&2x-3\end{bmatrix}$ & $B =\begin{bmatrix}3&6\\0&-1\end{bmatrix}$. If $AB =I$ (Where I is an identity matrix of order 2), then value of $x$ is

1

The correct answer is Option (2) → 1 **

$A=\begin{bmatrix}\frac{1}{3} & 2 \\ 0 & 2x-3\end{bmatrix}, \; B=\begin{bmatrix}3 & 6 \\ 0 & -1\end{bmatrix}$

$AB = \begin{bmatrix}\frac{1}{3}\cdot 3 + 2\cdot 0 & \frac{1}{3}\cdot 6 + 2\cdot(-1) \\[6pt] 0\cdot 3 + (2x-3)\cdot 0 & 0\cdot 6 + (2x-3)\cdot(-1)\end{bmatrix}$

$AB = \begin{bmatrix}1 & 2 - 2 \\ 0 & -(2x-3)\end{bmatrix}$

$AB = \begin{bmatrix}1 & 0 \\ 0 & 3 - 2x\end{bmatrix}$

For $AB = I$:

$3 - 2x = 1$

$2x = 2$

$x = 1$

The value of $x$ is 1.