DeterminantHard
Question
If A is a skew - symmetric matrix and n is an even positive integer, then An is
Options
A.a symmetric matrix
B.a skew-symmetric matrix
C.a diagonal matrix
D.none of these
Solution
AT = - A
(An)T = (AAA ------- A)T = (AT AT AT ------- AT) = (AT)n for all n ∈ N
(-A)n = (-1)n An
(An)T =
(An)T = (AAA ------- A)T = (AT AT AT ------- AT) = (AT)n for all n ∈ N
(-A)n = (-1)n An
(An)T =
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