AlgebraFree

Matrix Transpose Calculator

Transpose a 3x3 matrix by swapping rows and columns. Useful in many linear algebra transformations.

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Formula

(A^T)_{ij} = A_{ji}

The transpose flips a matrix across its main diagonal by swapping row and column indices.

Worked Example

A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]. A^T = [[1, 4, 7], [2, 5, 8], [3, 6, 9]].

Frequently Asked Questions

Does transposing change the determinant?

No. The determinant of A equals the determinant of A transpose.

What happens if I transpose twice?

Transposing twice returns the original matrix.

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