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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.

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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