Find the inverse of the following martrices by using transformation method.

Engineering

Mathematics

Algebra of Matrices

Inverse of a Matrix

Question

Find the inverse of the following martrices by using transformation method.
$[\begin{array}{cc} 1 & 2 \\ 2 & - 1 \end{array}]$

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

$[\begin{matrix} 1 & 2 & ⋮ & 1 & 0 \\ 2 & - 1 & ⋮ & 0 & 1 \end{matrix}] R_{2} \to R_{2} - 2 R_{1}$

$\Rightarrow [\begin{matrix} 1 & 2 & ⋮ & 1 & 0 \\ 0 & - 5 & ⋮ & - 2 & 1 \end{matrix}] R_{2} \to R_{2} / 5$

$\Rightarrow [\begin{matrix} 1 & 2 & ⋮ & 1 & 0 \\ 0 & 1 & ⋮ & 2 / 5 & - 1 / 5 \end{matrix}] R_{1} \to R_{1} - 2 R_{2}$

$\Rightarrow [\begin{matrix} 1 & 0 & ⋮ & - 4 / 5 & 2 / 5 \\ 0 & 1 & ⋮ & 2 / 5 & - 1 / 5 \end{matrix}]$

$\Rightarrow [\begin{matrix} 1 & 0 & ⋮ & 1 / 5 & 2 / 5 \\ 0 & 1 & ⋮ & 2 / 5 & - 1 / 5 \end{matrix}]$

$A^{- 1} = [\begin{array}{cc} 1 / 5 & 2 / 5 \\ 2 / 5 & - 1 / 5 \end{array}]$