Pick a matrix size, enter the values, and get the transpose instantly — rows become columns, columns become rows.
Matrix Transpose Calculator
How It’s Calculated
The transpose of a matrix flips it across its main diagonal — the entry in row i, column j of the original becomes the entry in row j, column i of the transpose. Unlike the inverse, the transpose always exists, for any matrix of any shape, square or not.
Worked Example
For A = [[1,2,3],[4,5,6],[7,8,9]], the transpose reads the columns of A as the rows of AT: AT = [[1,4,7],[2,5,8],[3,6,9]].
Frequently Asked Questions
Q: Does every matrix have a transpose?
Yes — even non-square matrices. An m×n matrix’s transpose is an n×m matrix. This tool is limited to square matrices for simplicity, since that’s what 2nd PUC and VTU questions mostly test.
Q: What’s a symmetric matrix?
A square matrix that equals its own transpose — A = AT. You can check any result above by comparing it to what you entered.
Transpose is one of the first operations covered in the 2nd PUC Matrices chapter. Read the full chapter guide →