Solving "What Matrix is This?" MCQ

[JonNash]

Homework Statement

The matrix
1 2 -3
2 5 -4
-3 -4 6
is a symmetric matrix by my reckoning. Although in this MCQ that is not an option. The options are
a)Hermitian
b)antisymmetric
c)orthogonal
d)idempotent

The Attempt at a Solution

Hermitian should have complex entities, we have none, so it is not Hermitian
antisymmetric should be -A=A^T and this does not obey that rule, so ruled out.
orthogonal should have A^T=A^-1 again not in this case
idempotent should be A*A=A, again this does not obey

So what should be the answer?

 

[Ray Vickson]

Homework Statement

The matrix
1 2 -3
2 5 -4
-3 -4 6
is a symmetric matrix by my reckoning. Although in this MCQ that is not an option. The options are
a)Hermitian
b)antisymmetric
c)orthogonal
d)idempotent

The Attempt at a Solution

Hermitian should have complex entities, we have none, so it is not Hermitian
antisymmetric should be -A=A^T and this does not obey that rule, so ruled out.
orthogonal should have A^T=A^-1 again not in this case
idempotent should be A*A=A, again this does not obey

So what should be the answer?

Who says the entries of the matrix are not complex? A real number is a complex number with imaginary part = 0.

 

[JonNash]

Who says the entries of the matrix are not complex? A real number is a complex number with imaginary part = 0.

Of course, stupid me. Then it is Hermitian since if I consider all img parts to be 0 then the matrix which I previously assumed to symmetric will just become a Hermitian since the conjugate of a matrix with img part=0 is itself. Thanks Ray.