Symmetric and Skew Symmetric Matrices

For the matrix A = `[(1,5),(6,7)]` verify that (A - A') is a skew symmetric matrix.

If A is symmetric matrix, then B′AB is ______.

If the matrix `((6,-"x"^2),(2"x"-15 , 10))` is symmetric, find the value of x.

Show that a matrix which is both symmetric and skew symmetric is a zero matrix.

The matrix  \[A = \begin{bmatrix}0 & - 5 & 8 \\ 5 & 0 & 12 \\ - 8 & - 12 & 0\end{bmatrix}\] is a 

If A and B are two matrices of order 3 × m and 3 × n respectively and m = n, then the order of 5A − 2B is 

Express the matrix A as the sum of a symmetric and a skew-symmetric matrix, where A = `[(2, 4, -6),(7, 3, 5),(1, -2, 4)]`

If \[A = \begin{bmatrix}1 & 2 \\ 0 & 3\end{bmatrix}\] is written as B + C, where B is a symmetric matrix and C is a skew-symmetric matrix, then B is equal to.