Let `A` and `B` be square matrices of the order `3xx3` . Is `(A B)^2=A^2B^2` ? Give reasons.

Let `A` and `B` be square matrices of the order `3xx3` . Is `(A B)^2=A^2B^2` ? Give reasons.

Monjur Alahi

6 views

2025-01-04 04:42

1 Answers

Salim Ahmed Kawsar

Since A and B are square matrices of order `3xx3`
`AB^(2)=AB AB`
=AB AB
=A A B B `[because AB =BA]`
`=A^(2)B^(2)`
So, `AB^(2)=A^(2)B^(2)` is true when AB=BA.

6 views Answered 2023-02-05 15:29

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