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:

2

The correct answer is Option (3) → 2

Given matrices:

$\begin{bmatrix} 1 & 0 \\ b & 5 \end{bmatrix} + 2 \begin{bmatrix} a & 0 \\ 1 & -2 \end{bmatrix} = I_2 = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$

Compute $2 \begin{bmatrix} a & 0 \\ 1 & -2 \end{bmatrix} = \begin{bmatrix} 2a & 0 \\ 2 & -4 \end{bmatrix}$

Add the matrices:

$\begin{bmatrix} 1+2a & 0+0 \\ b+2 & 5-4 \end{bmatrix} = \begin{bmatrix} 1+2a & 0 \\ b+2 & 1 \end{bmatrix}$

Equate to unit matrix:

$1 + 2a = 1 \Rightarrow 2a = 0 \Rightarrow a = 0$

$b + 2 = 0 \Rightarrow b = -2$

Value of $a - b = 0 - (-2) = 2$