If A is a skew-symmetric matrix of order 3- then the matrix A 4 isA- skew symmetricB- diagonalC- symmetricD- none of those

The correct option is C symmetric We have A^T = A (A^4)^T = (A.A.A.A.)^T = A^T A^T A^T A^T ⇒ ( A) ( A) ( A) ( A) = ( 1)^4 A^4 = A^4 ...

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Standard XII

Mathematics

Singular and Non Singualar Matrices

If A is a ske...

Question

If A is a skew-symmetric matrix of order 3, then the matrix $A^{4}$ is

skew symmetric

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symmetric

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diagonal

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none of those

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Solution

The correct option is B symmetric
We have $A^{T} = - A$
$(A^{4})^{T} = (A . A . A . A .)^{T} = A^{T} A^{T} A^{T} A^{T} \Rightarrow (- A) (- A) (- A) (- A) = (- 1)^{4} A^{4} = A^{4}$

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$I f m a t r i x A = [a_{i j}]_{3 \times 3}, m a t r i x B = [b_{i j}]_{3 \times 3} w h e r e a_{i j} + a_{j i} = 0 a n d b_{i j} - b_{j i} = 0, t h e n | A^{4} . B^{3} | i s$

I f m a t r i x A = [a_{i j}]_{3 \times 3}, m a t r i x B = [b_{i j}]_{3 \times 3} w h e r e a_{i j} + a_{j i} = 0 a n d b_{i j} - b_{j i} = 0, t h e n A^{4} . B^{3} i s

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

The correct option is B symmetric We have AT=−A (A4)T=(A.A.A.A.)T=ATATATAT⇒(−A)(−A)(−A)(−A)=(−1)4A4=A4

If A is a skew-symmetric matrix of order 3, then the matrix $A^{4}$ is

The correct option is B symmetric
We have $A^{T} = - A$
$(A^{4})^{T} = (A . A . A . A .)^{T} = A^{T} A^{T} A^{T} A^{T} \Rightarrow (- A) (- A) (- A) (- A) = (- 1)^{4} A^{4} = A^{4}$