Suppose A and B are both skew-symmetric matrices of the same size and alpha, beta is an element of C. Prove that alpha * A + Beta *B is a skew-symmetric matrix.

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Patrina SchowalterLv2

22 Jan 2019

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"A matrix A is said to be skew symmetric if A^T = - A.Show that if a matrix is skew symmetric, then its diagonal must allbe 0."
Where A^T works as such: say you have a 2x3 matrix suchthat row one is [ 1 2 3 ] and row two is [ 4 5 6 ]. Then the resultwould be a 3x2 matrix such that the first Column is 1, 2, 3 and thesecond Column is 4,5,6 {Sorry, can't seem to put matrices in here.}
I roughly understand how A^T=-A but I have no idea how toprove it and have been stuck on it for a couple days. Any helpwould be very much appreciated.

Please, I need help on #2, part a,b, and c. Thank you.

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