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  • Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 55 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 55 Maths Textbook Solution.

Answers (1)

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Answer: p=4

Hint: Here we use basic concept of matrix

Given: A=\begin{bmatrix} 2 & -2\\ -2 &2 \end{bmatrix} and A^{2}=pA Find p

Solution:

\begin{aligned} &\text { Here } A^{2}=A \times A \\ &=\left[\begin{array}{cc} 2 & -2 \\ -2 & 2 \end{array}\right] \times\left[\begin{array}{cc} 2 & -2 \\ -2 & 2 \end{array}\right] \\ &=\left[\begin{array}{cc} 4+4 & -4-4 \\ -4-4 & 4+4 \end{array}\right] \\ &A^{2}=\left[\begin{array}{cc} 8 & -8 \\ -8 & 8 \end{array}\right] \\ &A^{2}=p A \\ &{\left[\begin{array}{cc} 8 & -8 \\ -8 & 8 \end{array}\right]=p\left[\begin{array}{cc} 2 & -2 \\ -2 & 2 \end{array}\right]} \\ &\begin{array}{ll} 4\left[\begin{array}{cc} 2 & -2 \\ -2 & 2 \end{array}\right]=p\left[\begin{array}{cc} 2 & -2 \\ -2 & 2 \end{array}\right] \\ p =4 \end{array} \end{aligned}

 

 

 

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