I computed the adjugate of matrix A given, and then I used the formula (1/det|A|)*(adj A) to find the inverse of A.
This is the complete step-by-step solution (shown work) for exercise-11 found in section-3.3; (Cramers Rule, Volume, and Linear Transformations) contained within chapter-6; (Determinants) in the textbook, "Linear Algebra and it's Applications," David C. Lay; 2003, Pearson Education.
This textbook is currently used for Math-18 (Spring 2020) at the University of California, San Diego. Math-18 has a required prerequisite course completion with a "C" letter grade or higher--in Vector Calculus.
This is webpage has photos 1 through photo 6.
-Mark R. Rowe