This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Hey Gift, good to see you again. To find A^-1, we use the property that if AB = C, then A^-1 = BC^-1. Given AB = 3 & 2 \\ 1 & 1 and B = 1 & 1 \\ 2 & 0 . Let C = AB = 3 & 2 \\ 1 & 1 . Step 1: Calculate the determinant of C. For a 2 × 2 matrix a & b \\ c & d , the determinant is ad - bc. (C) = (3)(1) - (2)(1) = 3 - 2 = 1 Step 2: Calculate the inverse of C. For a 2 × 2 matrix a & b \\ c & d , the inverse is (1)/(ad-bc) d & -b \\ -c & a . C^-1 = (1)/(1) 1 & -2 \\ -1 & 3 = 1 & -2 \\ -1 & 3 Step 3: Calculate A^-1 using the formula A^-1 = BC^-1. A^-1 = 1 & 1 \\ 2 & 0 1 & -2 \\ -1 & 3 Step 4: Perform the matrix multiplication. A^-1 = (1