If A is a 3 3 × non-singular matrix such that AA A A T T = and B A AT = −1 , then BBT =
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Class 12
>>Applied Mathematics
>>Determinants
>>Inverse of Matrix
>>If A is an 3 × 3 non - singular matrix s
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If A is an 3×3 non-singular matrix such that AA
T
=A
T
A and B=A
A
T
, then BB
T
equals
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Correct option is D)
Given B=A
−1
A
T
Multiplying both side by A, we get BA=A
−1
A
T
A
⇒BA=A
−1
AA
T
,Since A
T
A=AA
T
⇒BA=A
T
Taking transpose both side, we get (BA)
T
=A
⇒A
T
B
T
=A
⇒B
T
=
A
T
A
⇒B
T
=
A
−1
A
T
A
−1
A
⇒B
T
=
B
I
∴BB
T
=I
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