I found the above answers either hard to read or too verbose, so I write one myself. And I think this is most intuitive way to implement transpose in linear algebra, you don't do value exchange, but just insert each element into the right place in the new matrix:
function transpose(matrix) {
const rows = matrix.length
const cols = matrix[0].length
let grid = []
for (let col = 0; col < cols; col++) {
grid[col] = []
}
for (let row = 0; row < rows; row++) {
for (let col = 0; col < cols; col++) {
grid[col][row] = matrix[row][col]
}
}
return grid
}