If A = bmatrix 2 & 0 & -1 5 & 1 & 0 0 & 1 & 3 bmatrix _ 3 3 , and A⁻¹ = bmatrix & -1 & 1 & 6 & -5 & -2 & 2 bmatrix _ 3 3 , then | | = _____ (where | | denotes the absolute value)

Step-by-step solution

The determinant of matrix A is: |A| = 2(1 3 - 0 1) - 0 + (-1)(5 1 - 1 0) = 6 - 5 = 1 Since |A| = 1 , the inverse of A is simply its adjugate matrix, A⁻¹ = adj (A) . The elements , , form the first column of A⁻¹ , which corresponds to the cofactors C₁₁, C₁₂, C₁₃ of the first row of matrix A . Calculating these cofactors: C₁₁ = (1)(3) - (0)(1) = 3 = 3 C₁₂ = -((5)(3) - (0)(0)) = -15 = -15 C₁₃ = (5)(1) - (1)(0) = 5 = 5 The product of these values is: = (-15) 5 3 = -225 Taking the absolute value: | | = |-225| = 225 Answ