Q. 685.0( 4 Votes )

Let A and B be sq

Answer :

Given that A and B are square matrices of the order 3 × 3.


We know (AB)2 = (AB)(AB)


(AB)2 = A × B × A × B


(AB)2 = A(BA)B


If the matrices A and B satisfy the commutative property for multiplication, then AB = BA.


We found (AB)2 = A(BA)B.


Hence, when AB = BA, we have (AB)2 = A(AB)B.


(AB)2 = A × A × B × B


(AB)2 = A2B2


Therefore, (AB)2 = A2B2 holds only when AB = BA.


Thus, (AB)2 ≠ A2B2 unless the matrices A and B satisfy the commutative property for multiplication.


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