#### Question

If A is a skew symmetric matric of order 3, then prove that det A = 0

#### Solution 1

If A is skew symmetric matric then `A^T = -A`

`:. |A| = -|A^T|`

|A| = - |A|

`=> 2|A| = 0`

`=>|A| = 0`

#### Solution 2

Let A be a skew-symmetric matrix of order 3.

Therefore, A^{T}=−A

∴ `|A^T| = |-A| = |A|`

⇒ |A| = |(-1)A|

We know that, |kA|=k^{n}|A|, where n is the order of the matrix

`=> |A| = (-1)^3 |A|`

`=> |A| = -|A|`

`=> |A| + |A| = 0`

`=> 2|A| = 0`

`=> |A| = 0`

Is there an error in this question or solution?

Solution If a is a Skew Symmetric Matric of Order 3, Then Prove that Det A = 0 Concept: Symmetric and Skew Symmetric Matrices.