If $A_{1},\ A_{3},\ \ldots,\ A_{2n - 1}$ are $n$ skew symmetric matrices of same order, then $B = \sum_{r = 1}^{n}{(2r - 1)\left( A_{2r - 1} \right)^{2r - 1}}$ will be

Question

Dr. Abubacker · Accepted Answer

(b)
$B = A_{1} + 3A_{3}^{3} + \cdots + (2n - 1)\left( A_{2n - 1} \right)^{2n - 1}$
$B^{T} = \left\lbrack A_{1} + 3A_{3}^{3} + \cdots + (2n - 1)\left( A_{2n - 1} \right)^{2n - 1} \right\rbrack$
$= - B$
Hence, B is skew-symmetric

Q. If $A_{1},\ A_{3},\ \ldots,\ A_{2n - 1}$ are $n$ skew symmetric matrices of same order, then $B = \sum_{r = 1}^{n}{(2r - 1)\left( A_{2r - 1} \right)^{2r - 1}}$ will be

Explanation

Reviewed by Dr. Abubacker

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