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What is the value of the determinant of the inverse of the matrix pmatrix -4 & -5 2 & 2 pmatrix ?

Options

  1. A1 2
  2. B1
  3. C2
  4. D4

Correct answer

A. 1 2

Step-by-step solution

Let A = pmatrix -4 & -5 2 & 2 pmatrix . The determinant of matrix A is given by: |A| = (-4)(2) - (-5)(2) |A| = -8 + 10 = 2 The determinant of the inverse of a matrix is the reciprocal of the determinant of the matrix, i.e., |A⁻¹| = 1 |A| . |A⁻¹| = 1 2 Answer: 1 2

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