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COMEDK202510 May 2025Morning ShiftMathematicsIndefinite IntegrationActual

For two matrices A and B , given that A⁻¹= 1 8 B then inverse of (8A) is

Options

  1. A1 64 B
  2. BB
  3. C1 8 B
  4. D8B

Correct answer

A. 1 64 B

Step-by-step solution

Given the relation A⁻¹ = 1 8 B . We need to find the inverse of the matrix (8A) . Using the property of matrix inversion (kA)⁻¹ = 1 k A⁻¹ for any non-zero scalar k , we have: (8A)⁻¹ = 1 8 A⁻¹ . Substituting the given expression for A⁻¹ into this equation: (8A)⁻¹ = 1 8 ( 1 8 B ) = 1 64 B . Answer: 1 64 B

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