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Need solution for RD Sharma maths class 12 chapter Algebra of matrices exercise 4.3 question 67 sub question (iii) math

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Answer: (A+B)(A-B) \neq A^{2}-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 (A+B)(A-B) \neq A^{2}-B^{2}

(A+B) (A-B)=A(A-B)+B(A-B)        [using distributive properties]    

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

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

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

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