If \(\begin{bmatrix}1&0\\b&5\end{bmatrix}+2\begin{bmatrix}a&0\\1&-2\end{bmatrix}=I\), where \(I\) is a unit matrix of order 2, then the value of \((a - b)\) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2
Adding the matrices on the left:
\( \begin{bmatrix}1+2a&0\\b+2&5-4\end{bmatrix} = \begin{bmatrix}1&0\\0&1\end{bmatrix} \)
Equal matrices have equal corresponding entries:
\(1 + 2a = 1,\quad a = 0\)
\(b + 2 = 0,\quad b = -2\)
\(a - b = 0 - (-2) = 2\)