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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

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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