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  4. If A is a skew symmetric matrix, then A2021 is

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Q. If $A$ is a skew symmetric matrix, then $A^{2021}$ is

KCETKCET 2022Matrices

Solution:

$A ^{ T }=- A$ or $A ^{ n }$ is slow symmetric if $n$ is odd
$P = A ^{2021}$
$P ^{ T }=\left[ A ^{2021}\right]^{ T }=\left[ A ^{ T }\right]^{2021}=(- A )^{2021}=- P$