2x2 Matrix Transpose Calculator

About this calculator

The transpose of a matrix, written Aᵀ, is formed by swapping its rows and columns: the entry in row 1, column 2 moves to row 2, column 1, and vice versa, while the diagonal entries (row 1, column 1 and row 2, column 2) stay exactly where they are. For a 2×2 matrix this simply means swapping the two off-diagonal entries.

Transposition is one of the most basic operations in linear algebra, used to convert a row vector into a column vector and back, to test whether a matrix is symmetric (a matrix equals its own transpose, A = Aᵀ), and as a building block in more advanced operations like computing a matrix's inverse or solving least-squares problems. In practical terms it shows up in computer graphics when switching between row-major and column-major conventions for transformation matrices, and in data science when reshaping a small feature matrix.

Enter the four entries of a 2×2 matrix, and the calculator returns its transpose.