If A = ((2x,0),(x,x)) and A ^{-1} = ((1,0),(-1,2)) then x = ? ​

Question

If A = \(​​​​\begin{pmatrix} 2x & 0 \\ x & x \\ \end{pmatrix}\)and A ^-1 = \(​​​​\begin{pmatrix} 1 & 0 \\ -1 & 2 \\ \end{pmatrix}\)then x = ?

A. 1 

B. 2 

C. 1/2

D. -2

Answer 1

We know that A x A ^-1 = I

\(​​​​\begin{pmatrix} 2x & 0 \\ x & x \\ \end{pmatrix}\) \(​​​​\begin{pmatrix} 1 & 0 \\ -1 & 2 \\ \end{pmatrix}\)= \(​​​​\begin{pmatrix} 1 & 0 \\ 0 & 1 \\ \end{pmatrix}\)

To satisfy the above condition 2x = 1

x = 1/2