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Let A and B be square matrices of the...

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

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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.
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