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Exercise 2.4.13

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Equation

AB = [\begin{matrix} a & 0 \\ c & 0 \end{matrix}] = BA = [\begin{matrix} a & b \\ 0 & 0 \end{matrix}]

gives $b = c = 0$ . Then $AC = CA$ gives $a = d$ . The only matrices that commute with $B$ and $C$ (and all other matrices) are multiples of $I : A = aI$ .

mathchakra

2021-12-06 17:32

Exercise 2.4.13

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