Olá!
Para encontrar a matriz inversa, usa-se a fórmula:
[tex]\frac{1}{ad-bc} \times \left[\begin{array}{cc}d&-b\\-c&a\\\end{array}\right][/tex]
Aplicando:
[tex]\frac{1}{1\times 2 - 3 \times 15} \times \left[\begin{array}{cc}2&-3\\-5&1\\\end{array}\right][/tex]
Multiplicando
[tex]\frac{1}{2-15} \times \left[\begin{array}{cc}2&-3\\-5&1\\\end{array}\right][/tex]
Subtraindo
[tex]-\frac{1}{13} \times \left[\begin{array}{cc}2&-3\\-5&1\\\end{array}\right][/tex]
Agora basta multiplicar na matriz
[tex]\left[\begin{array}{cc}2 \times (-\frac{1}{13}) &-3 \times (-\frac{1}{13}) \\-5 \times (-\frac{1}{13}) &1 \times (-\frac{1}{13} )\\\end{array}\right][/tex]
Multiplicando
[tex]\left[\begin{array}{cc}-\frac{2}{13} &\frac{3}{13} \\-\frac{5}{13} &-\frac{1}{13} \\\end{array}\right][/tex]
Matriz inversa
