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## How does this transpose matrix calculator work?

This transpose matrix calculator can assist you when trying to find the transpose of a matrix having from 1 to 4 rows and/or columns.

In algebra, the transpose (M^{T}) represents the matrix that results from switching the rows into columns and vice-versa of a given matrix (M).

For instance a matrix with 2 rows and 3 columns if transposed will result in one having 3 rows and 2 columns.

## Transpose matrix properties

1. (M^{T})^{T }= M

2.(M + N)^{T} = M^{T} + N^{T}

3. (MN)^{T} = N^{T}M^{T}

4. (scalar * M)^{T} = scalar * M^{T}

5. det(M^{T}) = det(M)

6. (M^{T})^{-1} = (M^{-1})^{T}