A 3x3 matrix A=[abcdefghi]\displaystyle {A}={\left[\begin{array}{ccc} {a}&{b}&{c}\\{d}&{e}&{f}\\{g}&{h}&{i}\end{array}\right]}A=⎣⎡adgbehcfi⎦⎤ is only invertible if ad−bc=0\displaystyle {a}{d}-{b}{c}={0}ad−bc=0 .
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