Question

Determine a matriz inversa da matriz a dada a matriz A = 1 1
2 3

Answer 1

A = $\left[\begin{array}{ccc}1&1\\2&3\end{array}\right]$ . $\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]$ . $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

a+c=1           b+d=0
2a+3c=0       2b+3d=1

a+c=1
a=1-c                   a=1-c
2.(10-c)+c=1        a=1-19
20-2c+c=1           a=-18
-c=1-20
c=19

b+d=0
b=-d             b=-d
2b+3d=1      b=-1
2.-d+3d=1
-2d+3d=1
d=1

Matriz inversa de A é: $\left[\begin{array}{ccc}-18&-1\\19&1\end{array}\right]$

Espero ter ajudado!

Answer 2

Inverte a diagonal principal e inverte o sinal a diagonal secundaria