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If A is a square matrix satisfying the equation A^2-5 A+7 I=0 , where I is the I dentity matrix and 0 is null matrix of same order, then A ⁻¹=

Options

  1. A1 7 (5 I - A )
  2. B1 7 ( ~A -5 I )
  3. C7(5 I-A)
  4. D1 5 (7 I - A )

Correct answer

A. 1 7 (5 I - A )

Step-by-step solution

Given aligned & A ^2-5 ~A +7 I =0 ( Multiply by A ⁻¹ both sides | A | 0 ) & A -5 I +7 ~A ⁻¹=0 & ~A ⁻¹= (5 I - A ) 7 aligned

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