use the given information to find A (matrix)

Question

I'm sorry guys, but i found nothing in my preceding section about solving an equation for a matrix variable like this, i understand each of the symbols, but what am I even supposed to do here? can you cancel out the inverse by taking the inverse of both sides, subtracting I and then dividing by 2?

Answer 1

You are sort of on the right track. Your situation is as follows: \begin{align*} (I+2A)^{-1} & = B\\ I+2A & = B^{-1}\\ 2A & = B^{-1}-I\\ A& = \frac{1}{2}\left(B^{-1}-I\right). \end{align*}

So this problem is all about doing matrix algebra and finding inverse.

Answer 2

Hint

$$\begin{pmatrix}a&b\\c&d\end{pmatrix}^{-1}=\frac{1}{ad-bc}\begin{pmatrix}d&-b\\-c&a\end{pmatrix}$$

Answer 3

Here is your solution. I am sorry ,but I am not good with Codecogs Typing.

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