Question

If A is a skew symmetric matrix of order 3 * 3 then tr(A)=​

Answer 1

Answer:

Step-by-step explanation:Since, A is a skew symmetric matrix

∴A

T

=−A

⇒∣A

T

∣=∣−A∣ ...(i)

⇒∣−A∣=(−1)

n

∣A∣

where n is the order.

∴∣−A∣=(−1)

3

∣A∣

=−∣A∣

Substituting in (i),

∣A

T

∣=−∣A∣

⇒−∣A∣=∣A

T

∣ ..(ii)

We also know for any matrix.

∣A∣=∣A

T

∣

replacing in (ii)

∴∣A∣=−∣A∣

⇒2∣A∣=0

⇒∣A∣=0