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Cómo comprender las preguntas y los. Estudios Bíoamericanos. USA Al Día.Q:
Why does a matrix of identity matrix sum to the identity?
Here is my question
How does a matrix of the form $$\begin{pmatrix}1&0\\0&1\end{pmatrix}+\begin{pmatrix}0&1\\1&0\end{pmatrix}+…+\begin{pmatrix}0&0\\0&0\end{pmatrix}$$
sum to the identity matrix?
I think that there exists some property of matrix that I don’t know that will help to understand this. Any hint is welcome.
Thanks.
A:
For any $n\times n$ matrix $M$, by definition $M^2=M$ and $M^{ -1}=M^{ -1}$, then we have
$$\begin{pmatrix}1&0\\0&1\end{pmatrix}\begin{pmatrix}1&0\\0&1\end{pmatrix}=\begin{pmatrix}1&0\\0&1\end{pmatrix}$$
$$\begin{pmatrix}1&0\\0
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