Given : A = \(\begin{bmatrix}
1& 3 &-1 \\[0.3em]
2& 2 & -1\\[0.3em]
3 & 0 & -1
\end{bmatrix}\) and B = \(\begin{bmatrix}
-2& 3 &-1 \\[0.3em]
-1& 2 & -1\\[0.3em]
-6 & 9& -4
\end{bmatrix}\)
Matrix A is of order 3 x 3 and Matrix B is of order 3 x 3
To show : matrix AB = BA
Formula used :
If A is a matrix of order a x b and B is a matrix of order c x d ,
then matrix AB exists and is of order a x d , if and only if b = c
If A is a matrix of order a x b and B is a matrix of order c x d ,
then matrix BA exists and is of order c x b , if and only if d = a
For matrix AB, a = 3,b = c = 3,d = 3 ,thus matrix AB is of order 3 x 3
For matrix BA, a = 3,b = c = 3,d = 3 ,thus matrix AB is of order 3 x 3
Matrix AB = Matrix BA = \(\begin{bmatrix}
1 & 0 & 0 \\[0.3em]
0 & 1 & 0\\[0.3em]
0 & 0& 1
\end{bmatrix}\)