Resposta:

8) a= 1 e b =0

a.b= I

[tex]\left[\begin{array}{ccc}1&0\\0&1\end{array}\right] . \left[\begin{array}{ccc}1&0\\0&1\end{array}\right] = \left[\begin{array}{ccc}1.1&0.0\\0.0&1.1\end{array}\right] = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex] (é uma matriz identidade)

9) a.b - [tex]\left[\begin{array}{ccc}1.3&2.1\\2.0&1.2\end{array}\right] = \left[\begin{array}{ccc}3&2\\0&2\end{array}\right][/tex]

10) é só realizar a contra ao contrario.

[tex](\frac{\left[\begin{array}{ccc}9&-23\\-2&-5\end{array}\right]}{\left[\begin{array}{ccc}1&-3\\2&-1\end{array}\right] }) - a\left[\begin{array}{ccc}-1&2\\3&0\end{array}\right] = b[/tex]

[tex]\left[\begin{array}{ccc}9/1&-23/(-3)\\-2/2&-5/(-1)\end{array}\right] = \left[\begin{array}{ccc}9-(-1)&7,6-2\\-1-3&5-0\end{array}\right] = \left[\begin{array}{ccc}10&5,6\\-4&5\end{array}\right][/tex]

b= [tex]\left[\begin{array}{ccc}10&5,6\\-4&5\end{array}\right][/tex]

11)

a)[tex]\left[\begin{array}{ccc}2.0&0.4\\6.2&7.(-8)\end{array}\right] - \left[\begin{array}{ccc}0.2&4.0\\2.6&-8.7\end{array}\right] = \left[\begin{array}{ccc}0&0\\0&0\end{array}\right][/tex]

b)Não é possível

c) [tex](\left[\begin{array}{ccc}-6.2&4.2&0.2\\1.2&1.2&4.2\\-6.2&0.2&6.2\end{array}\right]) - (\left[\begin{array}{ccc}6.3&9.3&-9.3\\-1.3&0.3&-4.3\\-6.3&0.3&-1.3\end{array}\right])= \left[\begin{array}{ccc}-30&-19&0\\5&2&20\\6&0&15\end{array}\right][/tex]

d)[tex](\left[\begin{array}{ccc}-6.(-6)&4.4&0.0\\1.1&1.1&4.4\\-6(-6)&0.0&6.6\end{array}\right])- (\left[\begin{array}{ccc}-6.6&4.9&0.(-9)\\1.(-1)&1.0&4(-4)\\-6.(-6)&0.0&6.(-1)\end{array}\right])=\left[\begin{array}{ccc}72&-20&0\\1&1&32\\0&0&18\end{array}\right][/tex]

12)

A.M=A.M

[tex]\left[\begin{array}{ccc}2.0&0.1\\6.(-1)&7.0\end{array}\right] = \left[\begin{array}{ccc}0.2&1.0\\-1.6&0.7\end{array}\right] resultado= \left[\begin{array}{ccc}0&0\\-6&0\end{array}\right] = \left[\begin{array}{ccc}0&0\\-6&0\end{array}\right][/tex]

B.M=M.B

[tex]\left[\begin{array}{ccc}0.0&4.1\\2.(-1)&-8.0\end{array}\right] = \left[\begin{array}{ccc}0.0&1.4\\-1.2&-0.(-8)\end{array}\right] Resultado= \left[\begin{array}{ccc}0&4\\-2&0\end{array}\right] = \left[\begin{array}{ccc}0&4\\-2&0\end{array}\right][/tex]

A.B=B.A

[tex]\left[\begin{array}{ccc}2.0&0.4\\6.2&7.(-8)\end{array}\right]= \left[\begin{array}{ccc}0.2&4.0\\2.6&-8.7\end{array}\right] resultado = \left[\begin{array}{ccc}0&0\\12&-56\end{array}\right]=\left[\begin{array}{ccc}0&0\\12&-56\end{array}\right][/tex]

13) Para mostrar que A é a matriz inversa de B é só multiplicar elas e o resultado tem que ser uma matriz identidade

[tex]\left[\begin{array}{ccc}1&1&0\\0&-1&2\\1&0&1\end{array}\right].\left[\begin{array}{ccc}-1&-1&2\\2&1&-2\\1&1&-1\end{array}\right]= \left[\begin{array}{ccc}1.(-1)&1.(-1)&0.2\\0.2&-1.1&2.(-2)\\1.1&0.1&1.(-1)\end{array}\right] =\left[\begin{array}{ccc}-1&-1&0\\0&-1&-4\\1&0&-1\end{array}\right].[/tex]

Não deu no resultado uma matriz identidade então A não é matriz inversa de B.