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  • Please solve RD Sharma class 12 chapter Algebra of matrices exercise 4.3 question 69 maths textbook solution

Please solve RD Sharma class 12 chapter Algebra of matrices exercise 4.3 question 69 maths textbook solution

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Answer: Hence proved (A+B)^{2}=A^{2}+2 A B+B^{2}

Hint: Matrix multiplication is only possible, when the number of columns of first matrix is equal to the number of rows of second matrix.

Given: A and B be square matrices of same order such that AB=BA

To prove: (A+B)^{2}=A^{2}+2 A B+B^{2}

Now, solving LHS gives

(A+B)^{2}=(A+B)(A+B)     [using distributive of matrix multiplication over addition]

                       \begin{array}{l} =A^{2}+A B+B A+B^{2} \\\\ =A^{2}+A B+A B+B^{2} \quad[\text { as } B A=A B] \\\\ =A^{2}+2 A B+B^{2} \end{array}

Therefore LHS=RHS

Hence, proved.

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