SOLUTION: Suppose that {{{A}}}, {{{B}}} and {{{A+B}}} are orthogonal matrices. Prove that {{{ (A+B)^-1 =A^-1 + B^-1}}} .

Question 1101998: Suppose that , and are orthogonal matrices. Prove that
.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Given Fact #1: Matrix is orthogonal. One property of orthogonal matrices is where is the transpose of matrix
Given Fact #2: Matrix is orthogonal. Similar to Fact #1, we know that,
Given Fact #3: Matrix is orthogonal. So we can say similar to the previous two facts above.

So,
(Fact #3)
Use the idea that (transpose of a sum is equal to the sum of transposes)
Substitution (Fact #1)
Substitution (Fact #2)
And that's all there is to it

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