Question

Write two matrices in the form ????a −b

b a
????.
a. Verify algebraically that the products of these two matrices are equal

Answer 1

Consider the matrices

`A=\left[\begin{array}{ccc}1&-3\\3&1\end{array}\right]` y
`B=\left[\begin{array}{ccc}4&2\\-2&4&\end{array}\right]`

Observe that

`AB=\left[\begin{array}{ccc}1&-3\\3&1\end{array}\right]\left[\begin{array}{cc}4&2\\-2&4\end{array}\right]=\left[\begin{array}{cc}10&-10\\10&10\end{array}\right]`

and

`BA=\left[\begin{array}{cc}4&2\\-2&4\end{array}\right]\left[\begin{array}{ccc}1&-3\\3&1\end{array}\right]=\left[\begin{array}{cc}10&-10\\10&10\end{array}\right]`