nicekikah

2020-10-26

Find DA and AD , if possible , where $D={D}_{g}\left(3,0,2,-1\right)$ and A is given matrix.
$A=\left[\begin{array}{cccc}2i& 0& 1& 3i\\ 0& 1+i& 8& 0\\ -i& 1& 0& i\\ 1& 1& 1& 1\end{array}\right]$

liingliing8

Step 1
The given matrices are
$A=\left[\begin{array}{cccc}2i& 0& 1& 3i\\ 0& 1+i& 8& 0\\ -i& 1& 0& i\\ 1& 1& 1& 1\end{array}\right]$
and
$D=\left[\begin{array}{cccc}3& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 2& 0\\ 0& 0& 0& -1\end{array}\right]$
As order of both the matrices are same so multiplication is possible.
Step 2
$AD=\left[\begin{array}{cccc}2i& 0& 1& 3i\\ 0& 1+i& 8& 0\\ -i& 1& 0& i\\ 1& 1& 1& 1\end{array}\right]\left[\begin{array}{cccc}3& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 2& 0\\ 0& 0& 0& -1\end{array}\right]$
$AD=\left[\begin{array}{cccc}6i& 0& 2& -3i\\ 0& 0& 16& 0\\ -3i& 0& 0& -i\\ 3& 0& 2& -1\end{array}\right]$
Now
$DA=\left[\begin{array}{cccc}3& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 2& 0\\ 0& 0& 0& -1\end{array}\right]\left[\begin{array}{cccc}2i& 0& 1& 3i\\ 0& 1+i& 8& 0\\ -i& 1& 0& i\\ 1& 1& 1& 1\end{array}\right]$
$DA=\left[\begin{array}{cccc}6i& 0& 3& 9i\\ 0& 0& 0& 0\\ -2i& 2& 0& 2i\\ -1& -1& -1& -1\end{array}\right]$

Jeffrey Jordon