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Question Number 55844 by gunawan last updated on 05/Mar/19

$$\mathrm{If}A\mathrm{is}\mathrm{an}\mathrm{involutory}\mathrm{matrix},\mathrm{then}$$$$(I+A)(I-A)=0.$$

Answered by 121194 last updated on 05/Mar/19

$$\mathrm{a}\mathrm{involutory}\mathrm{matrix}\mathrm{is}\mathrm{a}\mathrm{matrix}\mathrm{that}\mathrm{is}\mathrm{it}\mathrm{own}\mathrm{inverse}$$$$A^2=I$$$$(I+A)(I-A)=I^2-IA+AI-A^2$$$$=I^2-I$$$$=0$$

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