Question 160416
A) Since matrix A is {{{A=(matrix(2,2,a[11],a[12],a[21],a[22]))}}}, this means that 


 {{{A=(matrix(2,2,4,6,0,-1))}}}



B) The additive inverse of matrix A (let's call matrix B) will have elements that are additive inverses of the elements of matrix A. So the matrix is 


{{{B=(matrix(2,2,-4,-6,0,1))}}}



Note: simply change the signs of each element in matrix A to get matrix B.



Notice how {{{A+B=(matrix(2,2,4,6,0,-1))+(matrix(2,2,-4,-6,0,1))=(matrix(2,2,4+(-4),6+(-6),0+0,-1+1))=(matrix(2,2,0,0,0,0))}}} which is the zero matrix. So this confirms our answer.