Operation on 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

For two matrices $A \mathrm{and} B$, $AB=0$, If and only if

$A=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$. Verify closure property of matrix multiplication with scalar $-1$.

$A=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$. Verify closure property of matrix multiplication with scalar $4$.

$A=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$. Verify closure property of matrix multiplication with scalar $3$.

$A=\left[\begin{array}{cc}1& 4\\ 3& 2\end{array}\right]$ and $C=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ and $B$ is a matrix of order $2\times 2$. Prove the cancellation property of matrices and find matrix $B$.

$A=\left[\begin{array}{cc}1& 5\\ 3& 3\end{array}\right]$ and $C=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ and $B$ is a matrix of order $2\times 2$. Prove the cancellation property of matrices and find matrix $B$.

$A=\left[\begin{array}{cc}2& 4\\ 1& 6\end{array}\right]$ and $C=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ and $B$ is a matrix of order $2\times 2$. Prove the cancellation property of matrices and find matrix $B$.

$A=\left[\begin{array}{cc}1& 3\\ 4& 5\end{array}\right]$ and $C=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ and $B$ is a matrix of order $2\times 2$. Prove the cancellation property of matrices and find matrix $B$.

$A=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$ and $C=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ and $B$ is a matrix of order $2\times 2$. Prove the cancellation property of matrices and find matrix $B$.

$A=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$. Verify closure property of matrix multiplication with scalar $2$.

$A=\left[\begin{array}{cc}3& 7\\ 8& 5\end{array}\right]$. 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.