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  • Please Solve RD Sharma Class 12 Chapter 6 Adjoint and Inverse of a Matrix Exercise fill in the blaks Question 21 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 6 Adjoint and Inverse of a Matrix  Exercise fill in the blaks Question 21 Maths Textbook Solution.

Answers (1)

Answer \rightarrow A^{2}+B^{2}

Hint  \rightarrow AB=-BA

Given  \rightarrow B=-A^{-1}BA

Explanation \rightarrow A  & B are square matrices of same order

                \begin{aligned} &B=-A^{-1} B A \\ &A B=-A A^{-1} B A \end{aligned}

               AB=-I.BA                                    

              AB=-BA                                                        ...(i)

Now,

(A+B)^{2}=A^{2}+B^{2}+A B+B A

                   =A^{2}+B^{2}-B A+B A                                        from (i)

(A+B)^{2}=A^{2}+B^{2}

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