\(A =\begin{bmatrix}1/3&2\\0&2x-3\end{bmatrix}\) & \(B =\begin{bmatrix}3&6\\0&-1\end{bmatrix}\). If \(AB =I\) (Where I is an identity matrix of order 2), then value of \(x\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1
By matrix multiplication (row of A times column of B):
\( \displaystyle AB = \begin{bmatrix}\frac{1}{3}(3) + 2(0) & \frac{1}{3}(6) + 2(-1)\\ 0(3) + (2x-3)(0) & 0(6) + (2x-3)(-1)\end{bmatrix} \)
\( \displaystyle = \begin{bmatrix}1 & 0\\ 0 & 3 - 2x\end{bmatrix} \)
For \(AB = I\), the last entry must be 1:
\(3 - 2x = 1\)
\(x = 1\)