### Video Transcript

Given that the matrix ๐ด equals negative two, six, negative six, one, eight, four, find ๐ด transpose.

Just a quick reminder about this notation, first of all, when we see a matrix and then a superscript capital ๐, this means weโre being asked to find the transpose of the matrix ๐ด. Thatโs the matrix we get when we swap the rows and columns of the matrix ๐ด around.

Looking carefully at our matrix ๐ด, then, we can see that it has two rows and three columns. The matrix ๐ด transpose, then, will have three rows and two columns. The number of rows in matrix ๐ด is the number of columns in its transpose. And the number of columns in matrix ๐ด is the number of rows in its transpose.

The first row in matrix ๐ด โ so thatโs negative two, six, negative six โ becomes the first column in its transpose matrix. So, we can fill in this first column. The second row of matrix ๐ด โ so thatโs one, eight, four โ will become the second column in our matrix ๐ด transpose. So, by swapping the rows and columns of matrix ๐ด around, weโve found its transpose matrix. ๐ด transpose is equal to the matrix negative two, one, six, eight, negative six, four.

We can also look at individual elements of these two matrices. For example, the element that was in the first row and second column of matrix ๐ด โ so thatโs six โ is now in the second row and first column of the transpose matrix. Their positioning of rows and columns has been swapped around. Once again, our matrix ๐ด transpose is the three-by-two matrix negative two, one, six, eight, negative six, four.