 # 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.
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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
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