Algebra of Matrices

If matrix A = $\left[\begin{array}{cc}\text{a}& \text{b}\\ \text{c}& 1-\text{a}\end{array}\right]$ is such that A² = A. when $\text{bc}=1/4$ then a is equal to

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 $2\left(\begin{array}{c}1\\ 0\end{array}\begin{array}{c}3\\ x\end{array}\right)+\left(\begin{array}{c}y\\ 1\end{array}\begin{array}{c}0\\ 2\end{array}\right)=\left(\begin{array}{c}5\\ 1\end{array}\begin{array}{c}6\\ 8\end{array}\right)$.

$A=\left[\begin{array}{cc}2& 4\\ 6& 8\end{array}\right]$. Find $-$$A$.

$A=\left[\begin{array}{cc}2& 3\\ 1& 5\end{array}\right]$. Find $-$$A$.

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

$A=\left[\begin{array}{cc}3& 7\\ 8& 5\end{array}\right]$. Find sum of given matrix and its additive identity.

$A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$. Find sum of given matrix and its additive identity.

$A=\left[\begin{array}{cc}5& 6\\ 7& 8\end{array}\right]$. Find sum of given matrix and its additive identity.

$A=\left[\begin{array}{cc}3& 2\\ 5& 4\end{array}\right]$. Find sum of given matrix and its additive identity.

$A=\left[\begin{array}{cc}1& 2\\ 4& 6\end{array}\right]$. Find sum of given matrix and its additive identity.

$A=\left[\begin{array}{cc}5& 8\\ 3& 7\end{array}\right]$. Prove distributive property of scalar multiplication of a matrix with scalars $2$ and $3$.

$A=\left[\begin{array}{cc}7& 3\\ 5& 9\end{array}\right]$. Prove distributive property of scalar multiplication of a matrix with scalars $2$ and $3$.