Let A be a skew- symmetric matrix of odd order, then |A| is equal to

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3 and 4 .Determinants and Matrices

normal

Let $ A$ be a skew- symmetric matrix of odd order, then $ |A| $ is equal to

A

$0$

B

$1$

C

$-1$

D

None of these

Solution

(a) Let $A $ be a skew-symmetric matrix of odd order, say $(2n + 1)\,$.Since $ A$ is skew-symmetric, therefore ${A^T} = – A$.

$ \Rightarrow $ $|{A^T}|\, = \,| – A|\, \Rightarrow |{A^T}| = {( – 1)^{2n + 1}}|A|$

$ \Rightarrow $ $|{A^T}|\,\, = – |A|\, \Rightarrow |A| = – |A|$

$ \Rightarrow $ $2|A|\, = 0 \Rightarrow |A| = 0$.

Standard 12

Mathematics

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