if a is a square matrix of order 3 having a rope of zero then the determinant of a is
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12th
Maths
Determinants
Introduction to Determinants
If A is a square matrix of ...
MATHS
If A is a square matrix of order 3, then ∣(A−A
T
)
105
∣ is equal to
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ANSWER
∣
∣
∣
∣
(A−A
T
)
105
∣
∣
∣
∣
=
∣
∣
∣
−(A
T
−A)
∣
∣
∣
105
=−
∣
∣
∣
A
T
−A
∣
∣
∣
105
=−
∣
∣
∣
∣
(A
T
−A)
T
∣
∣
∣
∣
105
(∵ determinant of matrix and its transpose is equal)
=−
∣
∣
∣
A−A
T
∣
∣
∣
105
⇒
∣
∣
∣
A−A
T
∣
∣
∣
105
=−
∣
∣
∣
A−A
T
∣
∣
∣
105
=0(∵ determinant of skew-symmetric matrix of odd order is 0.)
∣
∣
∣
∣
(A−A
T
)
105
∣
∣
∣
∣
=0
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