Question 116768
{{{A=(matrix(2,2,-1,1,2,3))}}}
A matrix has an inverse if its determinant is not equal to zero. 
For a 2x2 matrix, 
{{{A=(matrix(2,2,a,b,c,d))}}}
The determinant is {{{abs(A)=ac-bd}}}
In this case the determinant is 
{{{abs(A)=ac-bd=(-1)(3)-(-1)(2)}}}
{{{abs(A)=-3+2}}}
{{{abs(A)=-1}}}
The inverse of a 2x2 matrix is given by,
{{{A^(-1)=(1/abs(A))*(matrix(2,2,d,-b,-c,a))}}}
In this case 
{{{A^(-1)=(1/abs(A))*(matrix(2,2,d,-b,-c,a))}}}
{{{A^(-1)=(1/-1)*(matrix(2,2,3,1,-2,-1))}}}
{{{A^(-1)=(matrix(2,2,-3,-1,2,1))}}}