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  • Explain solution for rd sharma class 12 chapter Algebra of matrices exercise 4.3 question 66 math

Explain solution for rd sharma class 12 chapter Algebra of matrices exercise 4.3 question 66 math

Answers (1)

Answer: (A+B)^{2}=A^{2}+2 A B+B^{2} does not hold

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

Solution: A

\begin{aligned} (A+B)^{2} =(A+B)(A+B) \\ \end{aligned}

                       = A(A+B)+B(A+B)          [using distributive property]
                       \begin{array}{l} =A A+A B+B A+B B \\ =A^{2}+A B+B A+B^{2} \end{array}

But,

(A+B)^{2}=A^{2}+2 A B+B^{2} is possible only when AB=BA

As we know  (x+y)^{2}=x^{2}+y^{2}+2 x y

Here, we can’t say that AB=BA

So,

(A+B)^{2}=A^{2}+2 A B+B^{2} does not hold

Posted by

infoexpert22

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