Math Calculators

Matrix Transpose Calculator (2×2)

Find the transpose of a 2×2 matrix by swapping its rows and columns.

Transpose (1,1) —

Transpose (1,2) —

Transpose (2,1) —

Transpose (2,2) —

About the Matrix Transpose Calculator (2×2)

The transpose of a matrix flips it over its main diagonal, turning rows into columns and columns into rows. For a 2×2 matrix [[a, b], [c, d]], the transpose swaps the off-diagonal entries b and c.

Formula: Transpose of [[a, b], [c, d]] = [[a, c], [b, d]]

Transposes are used throughout linear algebra, including in computing dot products, solving least-squares problems and working with symmetric matrices.