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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

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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