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Please solve RD Sharma class 12 chapter Algebra of matrices exercise 4.3 question 67 sub question (i) maths textbook solution

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Answer: In general matrix multiplication is not always commutative (A B \neq B A)(A+B)^{2} \neq A^{2}+ 2 A B+B^{2}

Hint: We use the formula (x+y)^{2}=x^{2}+y^{2}+2 x y

Given: A and B be square matrices of same order.

\\(A+B)^{2} =A^{2}+2 A B+B^{2}\\ \\(A+B)^{2} =(A+B)(A+B) \\\\

                       =A(A+B)+B(A+B)    [using distributive property ]              

                      \\=A \times A+A B+B A+B \times B \\\\ =A^{2}+A B+B A+B^{2} \\\\

(A+B)^{2} \neq A^{2}+2 A B+B^{2}

Since, in general matrix multiplication it is not always commutative (AB \neq BA )

So, (A+B)^{2} \neq A^{2}+ 2 A B+B^{2}

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