# Determine whether the statement, (A + B)^{-1} = A^{-1}+B^{-1}, assuming A, B, and A + B are invertible, is true or false. If the statement is false, make the necessary change(s) to produce a true statement.

boitshupoO 2021-03-02 Answered
Determine whether the statement, $\left(A+B{\right)}^{-1}={A}^{-1}+{B}^{-1}$, assuming A, B, and A + B are invertible, is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
You can still ask an expert for help

Expert Community at Your Service

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Available 24/7
• Math expert for every subject
• Pay only if we can solve it

## Expert Answer

unett
Answered 2021-03-03 Author has 119 answers
Step 1
Given:
$\left(A+B{\right)}^{-1}={A}^{-1}+{B}^{-1}$
To determine:
If A, B and (A+B) are invertible matrices then to check if the statement is True or False: Solution:The given statement is false as the given statement is not valid for all the invertible matrices:
Therefore, We can prove this using an example:
Step 2
Lets
###### Not exactly what you’re looking for?
Jeffrey Jordon
Answered 2022-01-24 Author has 2070 answers

Expert Community at Your Service

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Available 24/7
• Math expert for every subject
• Pay only if we can solve it