If A and B are square matrices of order n × n , then {(A - B)^2} is equal to

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3 and 4 .Determinants and Matrices

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If $A$ and $B$ are square matrices of order $n × n$, then ${(A - B)^2}$ is equal to

A

${A^2} - {B^2}$

B

${A^2} - 2AB + {B^2}$

C

${A^2} + 2AB + {B^2}$

D

${A^2} - AB - BA + {B^2}$

Solution

(d) 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.

Standard 12

Mathematics

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