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
Step 1: Identify the given matrix and the values of its elements. The matrix A is given as: A = a_11 & a_12 \\ a_21 & a_22 The given values for the elements are: a_11 = 1 a_22 = 1 a_21 = 2 a_12 = 2 Step 2: Substitute the given values into the matrix A. A = 1 & 2 \\ 2 & 1 Step 3: Calculate the determinant of A, denoted as |A|. For a 2 × 2 matrix a & b \\ c & d , the determinant is calculated as ad - bc. Applying this formula to matrix A: |A| = (1)(1) - (2)(2) |A| = 1 - 4 |A| = -3 Step 4: Compare the result with the given options. The calculated determinant is -3. This matches option D. The final answer is D. -3.