If A is a skew-symmetric matrix of order 3, then the matrix A 4 is Options: A . &nbspskew symmetric B . &nbspsymmetric C . &nbspdiagonal D . &nbspnone of those

If A is a skew-symmetric matrix of order 3, then the matrix A4 is

Question

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

A^{4}

Options:

A . skew symmetric

B . symmetric

C . diagonal

D . none of those

Answer: Option B
:
B
We are given that the matrix A is skew symmetric which implies that,

A^{T} = - A

--------(1)

(A^{4})^{T} = (A . A . A . A .)^{T} = A^{T} A^{T} A^{T} A^{T}

(By applying the property of transpose of a matrix)

\Rightarrow

(-A) (-A) (-A) (-A) (Using equation (1))

= (- 1)^{4} A^{4} = A^{4}

i.e,

(A^{4})^{T} = (A^{4})

A^{4}

is symmetric.

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