Question

The set of all 2x2 matrices of the form [a 1(top) 1 b(bottom)] with the standard matrix addition and scalar multiplication.

Answer 1

\[\mathbf {M}+\mathbf N=\begin{bmatrix}a&1\\1&b\end{bmatrix}+\begin{bmatrix}a&1\\1&b\end{bmatrix}=\begin{bmatrix}a+a&1+1\\1+1&b+b\end{bmatrix}\]

\[c\mathbf {M}=\begin{bmatrix}ca&c\\c&cb\end{bmatrix}\]