which is the inverse of this matrix?

Step-by-step explanation:

Many scientific and graphing calculators will compute this easily.

The inverse of a square matrix is a square matrix of the same dimensions. That eliminates choices C and D. We can check choices A and B by computing a couple of terms of the product of the given matrix and its "inverse". That product should be the identity matrix, with 1 on the diagonal and 0 elsewhere.

Using matrix A,

  (r, c) = (1, 1) = 1(-19) +2(15) +5(-2) = -19 +30 -20 = 1 . . . . correct

  (r, c) = (2,3) = 3(-7) +5(6) +9(-1) = -21 +30 =9 = 0 . . . . correct

Using matrix B,

  (r, c) = (1, 1) = 1(-19) +2(-2) +5(15) = -19 -4 +75 = 52 . . . . incorrect

Indications are that choice A is appropriate.