Question 174766
We know that the matrix has an inverse because the determinant is not equal to zero

[-3 1]
[-5 5]

[a  b]
[c  d]

To calculate the determinant ad-bc in this case -15+5=-10

Any Matrix inverse =1/ad-bc[d -b]
                           [-c a]

-1/10[5 -1]
     [5 -3]

To double check multiply the matrices together and see if you come up with the identity matrix.

[-3 1]-1/10[5 -1]
[-5 5]     [5  -3]

-15+5   3+3   -1/10[-10  0]

-25+25  5-15   -1/10[0  -10]


[1 0]
[0 1] is the identity matrix