Dear student, Let A=0000 AT=0000Since AT=A, A is a symmmetric matrix Now, -A=-0000 ⇒-A=0000Since AT=-A, A is a skew-symmetric matrix Thus, A=0000 is an example of a matrix that is both symmetric and skew-symmetric Regards

Please give answer.

Dear student,

Let A = [\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}] A^{T} = [\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}] Since A^{T} = A, A is a symmmetric matrix . Now, - A = - [\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}] \Rightarrow - A = [\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}] Since A^{T} = - A, A is a skew - symmetric matrix . Thus, A = [\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}] is an example of a matrix that is both symmetric and skew - symmetric .

Regards

View Full Answer