Given : A = \(\begin{bmatrix}
2& -3 & -5 \\[0.3em]
-1& 4 & 5 \\[0.3em]
1 & -3 & -4
\end{bmatrix}\) and B = \(\begin{bmatrix}
2& -2& -4 \\[0.3em]
-1& 3 & 4 \\[0.3em]
1 & -2 & -3
\end{bmatrix},\)
Matrix A is of order 3 x 3 and Matrix B is of order 3 x 3
To show : matrix AB = A, BA = B
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 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 = Matrix A
For matrix BA, a = 3,b = c = 3,d = 3 ,thus matrix AB is of order 3 x 3
MATRIX AB = A and MATRIX BA = B