Resposta:

É somar o subtrair cada termo da matriz:

[tex]\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] + \left[\begin{array}{ccc}e&f\\g&h\end{array}\right] = \left[\begin{array}{ccc}a+e&b + f\\c + g&d+h\end{array}\right][/tex]

B + B =

[tex]\left[\begin{array}{ccc}8&-2\\-5&1\end{array}\right] + \left[\begin{array}{ccc}8&-2\\-5&1\end{array}\right] = \left[\begin{array}{ccc}16&-4\\-10&2\end{array}\right][/tex]

B + A =

[tex]\left[\begin{array}{ccc}8&-2\\-5&1\end{array}\right] + \left[\begin{array}{ccc}1&0\\-2&4\end{array}\right] =\left[\begin{array}{ccc}9&-2\\-7&5\end{array}\right][/tex]

At = transposta de A onde as linhas de a são trocadas com as colunas

Então At = [tex]\left[\begin{array}{ccc}1&-2\\0&4\end{array}\right][/tex]

A + At =

[tex]\left[\begin{array}{ccc}1&0\\-2&4\end{array}\right] + \left[\begin{array}{ccc}1&-2\\0&4\end{array}\right] = \left[\begin{array}{ccc}2&-2\\-2&8\end{array}\right][/tex]

A - B =

[tex]\left[\begin{array}{ccc}1&0\\-2&4\end{array}\right]- \left[\begin{array}{ccc}8&-2\\-5&1\end{array}\right] = \left[\begin{array}{ccc}-7&2\\3&3\end{array}\right][/tex]