Given : A = \(\begin{bmatrix}
1 & 2 & 3 \\[0.3em]
0 & 1 & 0\\[0.3em]
1 & 1 & 0
\end{bmatrix}\) and B = \(\begin{bmatrix}
-1 & 1 & 0 \\[0.3em]
0 & -1 & 1\\[0.3em]
2 & 3 & 4
\end{bmatrix}\)
Matrix A is of order 3 x 3, and Matrix B is of order 3 x 3
To show : matrix AB \(\neq\) BA
The 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
Matrix AB =
For matrix BA, a = 3,b = c = 3,d = 3 ,thus matrix AB is of order 3 x 3
Matrix BA =
Matrix AB \(\neq\) BA