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Mathematics, 11.02.2020 21:19 gracie6313

Determine which of the following formulas hold for all invertible Γ—nΓ—n matrices A and B. 1. =AB=BA 2. +A+B is invertible 3. (+)2=2+2+2(A+B)2=A2+B2+2AB 4. (+)(+βˆ’1)=2++βˆ’1(I+A)(I+Aβˆ’1)=2I+A+Aβˆ’1 5. (βˆ’)(+)=βˆ’2(Iβˆ’A)(I+A)=Iβˆ’A2 6. ()βˆ’1=βˆ’1βˆ’1(AB)βˆ’1=Aβˆ’1Bβˆ’1 7. 3A3 is invertible 8. (βˆ’1)3=3βˆ’1(ABAβˆ’1)3=AB3Aβˆ’1 9. βˆ’1=ABAβˆ’1=B 10. (+)(βˆ’)=2βˆ’2

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Determine which of the following formulas hold for all invertible Γ—nΓ—n matrices A and B. 1. =AB=BA 2...
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