Question

please help me in this sum of maths exponents
solve the 5th and the 6th one

Answer 1

Answer:

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Answer 2

Answer:

4)

How do you prove that if (A+B) ^-1 = A^-1 + B^-1 then AB^-1A = BA^-1B?

Multiply both sides by A+B on the right, to get

I=A−1(A+B)+B−1(A+B)=I+A−1B+B−1A+I

and so

A−1B=−B−1A−I

Multiplying by B on the left, we get BA−1B=−A−B .

If we multiply by A+B on the left we get

I=(A+B)A−1+(A+B)B−1=I+BA−1+AB−1+I

and so

AB−1=−BA−1−I

Multiplying by A on the right, we obtain

AB−1A=−B−A

Since −B−A=−A−B , we conclude

AB−1A=BA−1B=−(A+B)

5) I can't solve 5 one

Hope 4 one is helpful to you

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