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Let A= [ array lll a & b & 1 2 & 1 & 3 1 & c & 2 array ] and A⁻¹= (5 A-A^2 ) , then:

Options

  1. A|A|=3
  2. B|A|=-3
  3. CTr (A)=5
  4. DTr (A)=a+b+c

Correct answer

D. Tr (A)=a+b+c

Step-by-step solution

aligned & 3 I=5 A^2-A^3 & A^3-5 A^2+3 I=0 & tr. (A)=5=a+3, a=2 & |A|=-3,4+2 c+3 b-1-6 c-4 b=-3, b+4 c=6 aligned and a+2+2 a-2 b-1-3 c=0,2 b+3 c=7,2 b+8 c=12, c=1, b=2

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