Final answer:
A symmetric matrix is equal to its transpose, while a skew-symmetric matrix has each element equal to the negative of its corresponding element in the transpose.
Step-by-step explanation:
In mathematics, a symmetric matrix is a square matrix that is equal to its transpose. This means that the entries in the matrix are symmetric about its main diagonal. For example, consider the matrix A = [[2, 3], [3, 4]]. This matrix is symmetric because A = AT.
On the other hand, a skew-symmetric matrix is a square matrix where each element is equal to the negative of its corresponding element in the transpose of the matrix. In other words, the entries in the matrix are anti-symmetric about its main diagonal. For example, consider the matrix B = [[0, 1, -2], [-1, 0, 3], [2, -3, 0]]. This matrix is skew-symmetric because B = -BT.