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Mathematics
Problem
Consider the matrices
A
=
(
1
2
0
0
1
3
0
0
1
)
A=\begin{pmatrix}1 & 2 & 0\\ 0 & 1 & 3\\ 0 & 0 & 1\end{pmatrix}
A
=
1
0
0
2
1
0
0
3
1
and
C
=
(
1
−
2
6
0
1
−
3
0
0
1
)
C=\begin{pmatrix}1 & -2 & 6\\ 0 & 1 & -3\\ 0 & 0 & 1\end{pmatrix}
C
=
1
0
0
−
2
1
0
6
−
3
1
. Show that
A
C
=
C
A
=
I
3
AC=CA=I_3
A
C
=
C
A
=
I
3
.
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