Question
If A is a 3×3 non-singular matrix such that AAT=ATAandB=A−1AT,then BBT is equal to
Answer: Option B
:
B
Given,AAT=ATAandB=A−1AT
We are asked for the value of the expression BBT.Since B is given in terms of A we will substitute for the values of BT and B.
BBT=(A−1AT)(A−1AT)T
=A−1ATA(A−1)T[∴(AB)T=BTAT]
=A−1AAT(A−1)T
=IAT(A−1)T[∴(A−1A)=I]
=(A−1A)T
=IT=I
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:
B
Given,AAT=ATAandB=A−1AT
We are asked for the value of the expression BBT.Since B is given in terms of A we will substitute for the values of BT and B.
BBT=(A−1AT)(A−1AT)T
=A−1ATA(A−1)T[∴(AB)T=BTAT]
=A−1AAT(A−1)T
=IAT(A−1)T[∴(A−1A)=I]
=(A−1A)T
=IT=I
Was this answer helpful ?
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