If A and B are arbitrary matrices, which of the matrices in Exercise 21 through 26 must be symmetric?
The matrix is not symmetric.
A matrix is symmetric if and only if it is equal to its transpose.
All entries above the main diagonal of a symmetric matrix are reflected into equal entries below the diagonal. A matrix is skew-symmetric if and only if it is the opposite of its transpose.
Thus, it gives
Therefore, if A and B are arbitrary matrices then the matrices is not symmetric.
Hence, the matrix is not necessarily symmetric.
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