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Show that , if A and B are square matric...

Show that , if A and B are square matrices such that AB=BA, then `(A+B)^(2)=A^(2)+2AB+B^(2)`.

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Since, A and B are square matrices duch that AB=BA
`(A+B)^(2)=(A+B)(A+B)`
`=A^(2)+AB+BA+B^(2)`
`=A^(2)+AB+AB+B^(2) [because AB=BA]`
`=A^(2)+2AB+B^(2)`
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