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Question
For the matrix A = `[(1, 5),(6, 7)]`, verify that (A – A') is a skew symmetric matrix.
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Solution
Given, A = `[(1, 5),(6, 7)]`
So, A' = `[(1, 6),(5, 7)]`
Now, (A – A') = `[(1, 5),(6, 7)] - [(1, 6),(5, 7)]`
= `[(1 - 1, 5 - 6), (6 - 5, 7 - 7)]`
= `[(0, -1), (1, 0)]`
Then, (A – A') `= [(0, 1), (-1, 0)] = - [(0, -1), (1, 0)]`
Since (A – A') = –(A – A'), it proves that the matrix (A – A') is a skew symmetric matrix.
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