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Inverse by elementary transformations

Transformations

Concept 2 of 11 in Matrices

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Think about this

The row operation R2→R2−2R1R_2 \to R_2 - 2R_1 turns [1021]\begin{bmatrix} 1 & 0 \\ 2 & 1 \end{bmatrix} into II. Can you use that to write down its inverse, with no formula?