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  • Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 20 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 20 Maths Textbook Solution.

Answers (1)

Answer: AA^{T} is symmetric matrix

Hint: Here we should know the concept of matrix, skew and skew-symmetric matrix

Given: AA^{T}is symmetric or skew symmetric if Ais square

Solution: Ais square matrix

Let Ais 2\times 2 matrix

So, A=\begin{bmatrix} 1 &3 \\ 2& 4 \end{bmatrix}

So, A\times A^{T}=\begin{bmatrix} 1 &3 \\ 2& 4 \end{bmatrix}\begin{bmatrix} 1 &2 \\ 3 &4 \end{bmatrix}

=\begin{bmatrix} 1+9 &2+12 \\ 2+12 & 4+16 \end{bmatrix}

=\begin{bmatrix} 10 &14 \\ 14 & 20 \end{bmatrix}

\left ( AA^{T} \right )^{T}=\begin{bmatrix} 10 &14 \\ 14 & 20 \end{bmatrix}

So, here we can say thatAA^{T}is symmetric matrix

 

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