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  • Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 56 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 56 Maths Textbook Solution.

Answers (1)

best_answer

Answer: 7A\left ( I+A \right )^{3}=-I

Hint: Here we use basic concept of square and identity matrix

Given:

A is square matrix A^{2}=A

7A\left ( I+A \right )^{3}=?

Solution:

\begin{aligned} &7 A-(I+A)^{3} \\ &=7 A-\left[I^{3}+A^{3}+3 I A(I+A)\right] \\ &=7 A-\left[I+A^{3}+3 A(I+A)\right] \\ &=7 A-\left[I+A^{3}+3 A I+3 A^{2}\right] \\ &=7 A-\left[I+A^{3}+3 A+3 A^{2}\right] \\ &=7 A-I-A^{3}-3 A-3 A^{2} \\ &=4 A-I-A^{3}-3 A^{2} \\ &=4 A-3 A-\left[A^{2} \times A\right]-I \quad\left[A^{2}=A\right] \\ &=4 A-3 A-[A \times A]-I \\ &=4 A-3 A-A-I \\ &=4 A-4 A-I \\ &7 A-(I+A)^{3}=-I \end{aligned}

 

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