MathAlgebraLinear algebraLinear operators

An inverse operator

Theory

The determinant of inverse matrix

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Consider a linear operator in a vector space R3\mathbb{R}^3:

Ax=(2x1−x2−2x3−x1+x2+2x3−2x1+x3)\mathcal{A}x = \begin{pmatrix} 2x_1 - x_2-2x_3 \\ -x_1 + x_2+2x_3 \\ -2x_1+x_3 \end{pmatrix}

where x=(x1,x2,x3)x = (x_1, x_2, x_3). What is the determinant of the matrix of A−1\mathcal{A}^{-1} equal to?

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