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Let A and B be non-singular square matrices of the same order. Consider the following statements.
(I) (AB)T = ATBT
(II) (AB)−1 = B−1A−1
(III) adj(AB) = (adj.A) (adj.B)
(IV) ρ(AB) =ρ(A)ρ(B)
(V) AB = A.B
Which of the above statements are false?
  • a)
    I, III & IV
  • b)
    IV & V
  • c)
    I & II
  • d)
    All of the above
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Let A and B be non-singular square matrices of the same order. Consid...
The correct statements are
Thus statements I, III and IV are wrong.
Free Test
Community Answer
Let A and B be non-singular square matrices of the same order. Consid...
The false statements are:
a) I, III
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Let A and B be non-singular square matrices of the same order. Consider the following statements.(I) (AB)T = ATBT(II) (AB)−1 = B−1A−1(III) adj(AB) = (adj.A) (adj.B)(IV) ρ(AB) =ρ(A)ρ(B)(V) AB = A.BWhich of the above statements are false?a)I, III & IVb)IV & Vc)I & IId)All of the aboveCorrect answer is option 'A'. Can you explain this answer?
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