A) \[{{A}^{2}}-{{B}^{2}}\]
B) \[{{A}^{2}}-2AB+{{B}^{2}}\]
C) \[{{A}^{2}}+2AB+{{B}^{2}}\]
D) \[{{A}^{2}}-AB-BA+{{B}^{2}}\]
Correct Answer: D
Solution :
Given, A and B are square matrices of order n × n. We know that \[{{(A-B)}^{2}}=(A-B)\,\,(A-B)\] \[={{A}^{2}}-AB-BA+{{B}^{2}}\] Note that \[AB\ne BA\] in general.
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