imo class 12 determinants

If A = diag(d1, d2, d3) and no element is zero, what is A⁻¹?

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If A = diag(d1, d2, d3) and no element is zero, what is A⁻¹?

  • A. diag(1/d1, 1/d2, 1/d3)
  • B. diag(-d1, -d2, -d3)
  • C. A itself
  • D. I

Answer: A) diag(1/d1, 1/d2, 1/d3)

Explanation: The inverse of a diagonal matrix is simply the diagonal matrix of the reciprocals of its diagonal elements.

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