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Determinants
Question
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If A is a 3x3 non- singular matrix such that AAT = ATA, then BBT is equal to

  • l +B
  • l

  • B-1

  • (B-1)T

Answer

B.

l

If A is non - singular matrix then |A| ≠0
AAT = ATA and B = A-1AT
BBT = (A-1AT)(A-1AT)T
= A-1ATA(A-1)T       [∵ (AB)T= BTAT]
=A-1AAT(A-1)T        [∵ AAT = ATA]
=AT(A-1)T              [ ∵A-1A = l]
=A-1A)T                 [∵ (AB)T = BTAT]
lT = l

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