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  • Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 44 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 44 Maths Textbook Solution.

Answers (1)

Answer: \left ( I+A \right )^{2}-3A=I

Hint: Here we use the basic knowledge of identity and square matrix

Given:

 I is a identity matirx

A is a square matrix

A^{2}=A then find the value of\left ( I+A \right )^{2}-3A

Solution:

\begin{aligned} I \text { is a identity } & \text { matrix }=(I+A)^{2}-3 A=(I+A) \times(I+A)-3 A \\ &=[I * I+A * I+I * A+A * A] \\ &-3 A[\text { using matrix distributing law } A(B+C)=A B+A C] \\ &=\left[I+A+A+A^{2}\right]-3 A=I+2 A+A-3 A=I+3 A-3 A=I \end{aligned}

So, \left ( I+A \right )^{2}-3A=I

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