Question 172192
The determinant of the general 2x2 matrix {{{(matrix(2,2,a,b,c,d))}}} is {{{D=a*d-b*c}}}



So in this case, the matrix {{{(matrix(2,2,5,2,-3,1))}}} gives us the values {{{a=5}}}, {{{b=2}}}, {{{c=-3}}}, and {{{d=1}}}



{{{D=a*d-b*c}}} Start with the determinant of any 2x2 matrix



{{{D=5*1-2*(-3)}}} Plug in {{{a=5}}}, {{{b=2}}}, {{{c=-3}}}, and {{{d=1}}}



{{{D=5+6}}} Multiply



{{{D=11}}} Add



So the determinant of the matrix {{{(matrix(2,2,5,2,-3,1))}}} is 11