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$If A is a 3 \times 3 non-singular matrix such that A A^{T} = A^{T} A and B = A^{- 1} A^{T}, then B B^{T} =$

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Correct option is B

Given, AAT=ATA and B=A−1ATBBT=A−1ATA−1ATT=A−1ATAA−1T ∵(AB)T=BTAT=A−1AATA−1T ∵AAT=ATA=IATA−1T ∵A−1A=I=ATA−1T=A−1AT ∵(AB)T=BTAT=IT=I

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If A is a 3×3 non-singular matrix such that AAT=ATA and B=A−1AT, then BBT=

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

$If A is a 3 \times 3 non-singular matrix such that A A^{T} = A^{T} A and B = A^{- 1} A^{T}, then B B^{T} =$