If matrix A = [[2, 3], [1, 4]], what is the determinant of matrix A and its inverse A^(-1)?

Answer and explanation

Correct answer: B. det(A) = 5; A^(-1) = [[4/5, -3/5], [-1/5, 2/5]]

  1. Step 1: The determinant of a 2x2 matrix [[a, b], [c, d]] is det(A) = ad - bc.
  2. Step 2: Here, det(A) = (2)(4) - (3)(1) = 8 - 3 = 5.
  3. Step 3: The formula for the inverse is A^(-1) = (1 / det(A)) * [[d, -b], [-c, a]].
  4. Step 4: Substitute values: A^(-1) = (1/5) * [[4, -3], [-1, 2]] = [[4/5, -3/5], [-1/5, 2/5]].
Answer
det(A) = 5; A^(-1) = [[4/5, -3/5], [-1/5, 2/5]].
Why not the others: 'det(A) = -5' reverses the subtraction order; '[[2/5, -3/5], [-1/5, 4/5]]' forgets to swap the main diagonal elements a and d; 'det(A) = 11' incorrectly adds ad + bc.

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