2×2 Matrix Transpose Calculator
Transpose a 2×2 matrix online. Enter your entries and get the 2×2 transpose instantly, with each row of Aᵀ built from the matching column of A.
Enter a 2×2 matrix below and read off its 2×2 transpose. The grid is already sized for you, and every entry updates the result as you type.
What changes and what does not
Transposing a 2×2 matrix produces a 2×2 matrix. The entries themselves are untouched — only their positions change, with aij moving to (j, i). Entries on the main diagonal stay exactly where they are, which is why a symmetric matrix looks identical after transposing.
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Frequently asked questions
What are the dimensions of a 2×2 matrix after transposing? ▾
A 2×2 matrix transposes to a 2×2 matrix — square matrices keep their shape, though the entries still move.
How do you transpose a 2×2 matrix by hand? ▾
Write the first row of the original as the first column of the result, the second row as the second column, and so on until all 2 rows have become columns.
When does a 2×2 matrix equal its own transpose? ▾
When it is symmetric — that is, when the entry in row i, column j matches the entry in row j, column i for every pair. Mirror the entries across the main diagonal and nothing changes.
About this Calculator
Transpose a 2×2 matrix online. Enter your entries and get the 2×2 transpose instantly, with each row of Aᵀ built from the matching column of A.