Systems, apparatuses, and methods for performing in-place matrix transpose operations are disclosed. Operations for transposing tiles of a matrix are scheduled in an order determined by moving diagonally through tiles of the matrix. When a diagonal line hits a boundary, then a tile on a new diagonal line of the matrix is selected and operations are scheduled for transposing this tile. Only tiles within a triangular region of the matrix are scheduled for being transposed. This allows memory access operations to be performed in parallel, expediting the matrix transpose operation compared to linear tile indexing.