If \( \mathrm{A}=\begin{bmatrix}\frac{1}{4} & 2\\0 & 2x-3\end{bmatrix} \), \( \mathrm{B}=\begin{bmatrix}4 & 8\\0 & -1\end{bmatrix} \) and AB = I2 (Identity matrix of order 2), then the value of \( x \) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1
Multiplying row by column:
\( \displaystyle AB=\begin{bmatrix}\frac{1}{4}(4)+2(0) & \frac{1}{4}(8)+2(-1)\\0(4)+(2x-3)(0) & 0(8)+(2x-3)(-1)\end{bmatrix} \)
\( \displaystyle =\begin{bmatrix}1 & 0\\0 & 3-2x\end{bmatrix} \)
Comparing with \( I_2 \), the entry in the second row and second column must be 1:
\( \displaystyle 3-2x=1 \)
\( \displaystyle x=1 \)