Matrix Theory

Show that each matrix type is normal.

1. Hermitian
2. skew-Hermitian
3. unitary
4. symmetric
5. skew-symmetric
6. orthogonal

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...al.)
Now use the definitions for the six cases stated and plug them into the above definition to show they are normal:
1. Hermitian, A^t = A , so
[A , A^t] = A A^t - A^t A = A A - A A = 0
2. skew-Hermitian, A^t = -A , so
[A , A^t] = A A^t - A^t A = - A A + A A = 0
3. unitary, A^t = A^i
[A , A^t] = A A^t - A^t A = A ...