If A is a 3×3 non-singular matrix such that AAT=ATAandB=A−1AT,thenBBT is equal to
Options:
A .  
I + B
B .  
I
C .  
B−1
D .  
(B−1)T
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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