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To find the transpose of a matrix, the rows of the matrix are written as the new columns of the transposed matrix. Alternatively this is the same as writing the columns of a matrix as the rows of the transposed matrix.
The transpose of a matrix is simply a flipped version of the original matrix. We can transpose a matrix by switching its rows with its columns.
The symbol is a "T" placed above and to the right like this: Aᵗ
In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose.

Square matrix A is said to be skew-symmetric if aᵢⱼ =−aⱼᵢ for all i and j. In other words, we can say that matrix A is said to be skew-symmetric if transpose of matrix A is equal to negative of matrix A i.e (Aᵗ =−A). Note that all the main diagonal elements in the skew-symmetric matrix are zero.

It is also important to note that if a matrix has dimensions n×m then the transposed matrix will have dimensions m×n
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