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  • Please Solve RD Sharma Class 12 Chapter 6 Adjoint and Inverese of Matrices Exercise Fill in the blanks Question 1 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 6 Adjoint and Inverese of Matrices Exercise Fill in the blanks Question 1 Maths Textbook Solution.

Answers (1)

Answer  \rightarrow I_{n}

Hint   \rightarrow A^{-1}=adj A/\left | A \right |

Given  \rightarrow A   is a unit matrix of order n  then  A\left ( adj A \right )=

Explanation:  A is a unit matrix of order  n \Rightarrow \left | A \right |=1

Now,

                 \begin{aligned} &A^{-1}=(\operatorname{adj} A) /|A| \\\\ &A A^{-1}=A(\operatorname{adj} A) /|A| \end{aligned}

                I_{n \times n}=A(\operatorname{adj} A) /|A|                                  \left[_{\mathrm{as}}|A|=1\right]

                A(\operatorname{adj} A)=I_{n \times n}.

Hence,

                A(\operatorname{adj} A)=I_{n \times n}

Remarks:   A(\operatorname{adj} A)=I_{n \times n}  where  A  is a unit matrix of order  n.

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