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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

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