Question
Asked Dec 28, 2019
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A matrix M ∈Mn×n(C) is called skew-symmetric if Mt= −M. Prove that if M is skew-symmetric and n is odd, then M is not invertible. What happens if n is even?

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Expert Answer

Step 1

The matrix is not invertible if its determinant is 0.

If k is multiplied to the matrix Anxn then,

Advanced Math homework question answer, step 1, image 1
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Step 2

Assume M is skew symmetric. So,

M’=-M

Take the determinant of both sides.

Advanced Math homework question answer, step 2, image 1
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Step 3

If n is odd, then (-1)...

Advanced Math homework question answer, step 3, image 1
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