Algebra of Matrices

Find the value of $x$ and $y$ that satisfies the equations $\left[\begin{array}{cc}3& -2\\ 3& 0\\ 2& 4\end{array}\right]\left[\begin{array}{cc}y& y\\ x& x\end{array}\right]=\left[\begin{array}{cc}3& 3\\ 3y& 3y\\ 10& 10\end{array}\right]$

The value of $x+y$ from the following equation is $2\left(\begin{array}{c}1\\ 0\end{array}\begin{array}{c}3\\ x\end{array}\right)+\left(\begin{array}{c}y\\ 1\end{array}\begin{array}{c}0\\ 2\end{array}\right)=\left(\begin{array}{c}5\\ 1\end{array}\begin{array}{c}6\\ 8\end{array}\right)$.

Check weather given matrices of the order $3\times 3$ and $2\times 2$ are to be comparable or not?

$A=\left[\begin{array}{cc}6& 7\\ 5& 2\end{array}\right]$. Find additive inverse of $A$.

$A=\left[\begin{array}{cc}1& 4\\ 3& 5\end{array}\right]$. Find additive inverse of $A$.

$A=\left[\begin{array}{cc}2& 1\\ 4& 6\end{array}\right]$. Find additive inverse of $A$.

If $A=\left[\begin{array}{cc}7& 8\\ 5& 6\end{array}\right]$, $B=\left[\begin{array}{cc}4& 5\\ 2& 3\end{array}\right]$ and $C=\left[\begin{array}{cc}1& 2\\ 4& 3\end{array}\right]$. Prove the associative property of addition.

If $A=\left[\begin{array}{cc}2& 3\\ 5& 7\end{array}\right]$, $B=\left[\begin{array}{cc}6& 4\\ 2& 3\end{array}\right]$ and $C=\left[\begin{array}{cc}1& 3\\ 2& 4\end{array}\right]$. Prove the associative property of addition.

If $A=\left[\begin{array}{cc}1& 3\\ 5& 6\end{array}\right]$, $B=\left[\begin{array}{cc}4& 5\\ 1& 2\end{array}\right]$ and $C=\left[\begin{array}{cc}3& 1\\ 4& 3\end{array}\right]$. Prove the associative property of addition.

If $A=\left[\begin{array}{cc}1& 2\\ 4& 6\end{array}\right]$, $B=\left[\begin{array}{cc}2& 4\\ 5& 3\end{array}\right]$ and $C=\left[\begin{array}{cc}0& 1\\ 2& 3\end{array}\right]$. Prove the associative property of addition.

If $A=\left[\begin{array}{cc}5& 7\\ 6& 8\end{array}\right]$, $B=\left[\begin{array}{cc}2& 4\\ 1& 3\end{array}\right]$. Prove the closure property of addition.

If $A=\left[\begin{array}{cc}2& 3\\ 8& 6\end{array}\right]$, $B=\left[\begin{array}{cc}1& 2\\ 3& 5\end{array}\right]$. Prove the closure property of addition.

If $A=\left[\begin{array}{cc}1& 7\\ 2& 3\end{array}\right]$, $B=\left[\begin{array}{cc}3& 6\\ 5& 8\end{array}\right]$. Prove the closure property of addition.

If $A=\left[\begin{array}{cc}1& 2\\ 4& 6\end{array}\right]$, $B=\left[\begin{array}{cc}2& 4\\ 5& 3\end{array}\right]$. Prove the closure property of addition.

Let $A=\left[\begin{array}{rr}1& 3\\ 4& -3\end{array}\right]$, Let $S=\left\{\left[\begin{array}{l}x\\ y\end{array}\right]\in R^2/A\left[\begin{array}{l}x\\ y\end{array}\right]=3\left[\begin{array}{l}x\\ y\end{array}\right]\right\}$what is the cardinality of $S$ ?