The transpose of the matrix A {\displaystyle A} is equal to A T = [ 1 − 2 3 1 ] . {\displaystyle A^{T}=\left[{\begin{array}{cc}1&-2\\3&1\end{array}}\right].}
By matrix multiplication we have C = A B = [ 9 13 − 4 − 5 ] {\displaystyle C=AB=\left[{\begin{array}{cc}9&13\\-4&-5\end{array}}\right]}
and then A B A T = C A T = [ 9 13 − 4 − 5 ] [ 1 − 2 3 1 ] = [ 48 − 5 − 19 3 ] . {\displaystyle ABA^{T}=CA^{T}=\left[{\begin{array}{cc}9&13\\-4&-5\end{array}}\right]\left[{\begin{array}{cc}1&-2\\3&1\end{array}}\right]=\color {blue}{\left[{\begin{array}{cc}48&-5\\-19&3\end{array}}\right]}.}
is equal to ![{\displaystyle A^{T}=\left[{\begin{array}{cc}1&-2\\3&1\end{array}}\right].}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/82562f8842a3712849dc50616b33fa17c968ba4d)
![{\displaystyle C=AB=\left[{\begin{array}{cc}9&13\\-4&-5\end{array}}\right]}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/2eea07eb8efe4d3e27fda59b081f07c506407e86)
![{\displaystyle ABA^{T}=CA^{T}=\left[{\begin{array}{cc}9&13\\-4&-5\end{array}}\right]\left[{\begin{array}{cc}1&-2\\3&1\end{array}}\right]=\color {blue}{\left[{\begin{array}{cc}48&-5\\-19&3\end{array}}\right]}.}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/c7872472c45fbf6050d430fbeeae2002794d630f)
