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The characteristic equations of a (3 x 3) matrix A is defined as a(λ) = | λ | - Al = λ3 + λ+ 2λ + 1 = 0. If l denotes identity matrix, then the inverse of matrix A will be
  • a)
    A2 + A + 2l
  • b)
    A2 +A + l
  • c)
    -(A2 +A + l)
  • d)
    -(A+ A + 2l)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The characteristic equations of a (3 x 3) matrix A is defined as a(&la...
We are given that the characteristic equation of a 3 x 3 matrix ,A is
λ+ λ2 + 2λ + 1 = 0
By Cayley Hamilton theorem, this characteristic equations may be written in the matrix form as,
A3 + A2+ 2A + I=0
or A3 + A2 + 2A = - I
or A(A2 + A + 2I) = - I
or A-1 = - (A2 + A + 2I)
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Most Upvoted Answer
The characteristic equations of a (3 x 3) matrix A is defined as a(&la...
We are given that the characteristic equation of a 3 x 3 matrix ,A is
λ+ λ2 + 2λ + 1 = 0
By Cayley Hamilton theorem, this characteristic equations may be written in the matrix form as,
A3 + A2+ 2A + I=0
or A3 + A2 + 2A = - I
or A(A2 + A + 2I) = - I
or A-1 = - (A2 + A + 2I)
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The characteristic equations of a (3 x 3) matrix A is defined as a(λ) = | λ | - Al = λ3 + λ2+ 2λ + 1 = 0. If ldenotes identity matrix, then the inverse of matrix A will bea)A2+ A + 2lb)A2+A + lc)-(A2 +A + l)d)-(A2+ A + 2l)Correct answer is option 'D'. Can you explain this answer?
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