### Video Transcript

Given that 𝐴 is a matrix of order two by two, with 𝑎 one one equal to seven, 𝑎 one two equal to negative 10, 𝑎 two one equal to negative nine, and 𝑎 two two equal to two, find the matrix 𝐴.

We’re told that the matrix 𝐴 is of order two by two, which means that it has two rows and two columns. It therefore has four elements that we need to complete. The notation 𝑎 and then a subscript 𝑚 and 𝑛 is used to denote the element in row 𝑚 and column 𝑛 of the matrix 𝐴.

We’re told, first of all, that the element 𝑎 one one is equal to seven. This is the element in the first row and first column of the matrix. So we can fill in seven in its correct place in the matrix.

Next, we’re told that 𝑎 one two is equal to negative 10. This is the element in the first row and second column of the matrix 𝐴. So we can fill this element in. 𝑎 two one is equal to negative nine. This is the element in the second row and first column of the matrix.

Finally, we consider the fourth element of the matrix, 𝑎 two two. 𝑎 two two is the element in the second row and second column of the matrix, which is the only gap that we’ve got left to complete. The matrix 𝐴 is the matrix with first row seven, negative 10 and second row negative nine, two.