If A is a skew-symmetric matrix of order 3, then the value of |A| is:

Question

If A is a skew-symmetric matrix of order 3, then the value of $| A |$ is:

Smart Achievers · Accepted Answer

(2)

Ans. 0

Explanation:

Since, A is a skew-symmetric matrix,

$∴$ $A^{T} = - A$

$\Rightarrow$ $| A^{T} |$ $=$ $| - A |$

Since $| A^{T} |$ $=$ $| A |$ and for a $3 \times 3$ matrix,

$| - A |$ $= {(- 1)}^{3}$ $| A |$ $,$

we get $| A |$ $= {(- 1)}^{3}$ $| A |$

Hence, $| A |$ $= -$ $| A |$ $,$

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

$\Rightarrow$ $| A |$ $= 0$

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