# If A and B are two equal ordered matrix such that AB = BAthen prove that (A+B) (A-B) = A2-B2 (A-B)2= A2-2AB+B2 (A+B)3= A3+3A2B+3AB2+B3

given : AB = BA
​1.
LHS of the given equation is:
$\left(A+B\right)\left(A-B\right)={A}^{2}+BA-AB-{B}^{2}\phantom{\rule{0ex}{0ex}}={A}^{2}+AB-AB-{B}^{2}\phantom{\rule{0ex}{0ex}}={A}^{2}-{B}^{2}$
= RHS
2.
LHS of the given equation is:
$\left(A-B{\right)}^{2}=\left(A-B\right)\left(A-B\right)\phantom{\rule{0ex}{0ex}}={A}^{2}-BA-AB+{B}^{2}\phantom{\rule{0ex}{0ex}}={A}^{2}-AB-AB+{B}^{2}\phantom{\rule{0ex}{0ex}}={A}^{2}-2AB+{B}^{2}$
= RHS
3.
LHS of the given equation is:

= RHS
hope this helps you.

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