Matrices Test -...

If $$\begin{bmatrix} 5 & x & 1 \end{bmatrix} \begin{bmatrix} 2 \\ -1 \\ 3 \end{bmatrix}  = (20)$$, then the value of $$x$$ is

Let $$A = \begin{bmatrix}x + y & y\\ 2x & x - y\end{bmatrix}, B = \begin{bmatrix} 2& -1\end{bmatrix}$$ and $$C = \begin{bmatrix} 3& 2\end{bmatrix}.$$ If $$AB = C$$, then $$A^{2}$$ is equal to

Choose the correct statement related to the matrices $$A=\begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}$$ and $$B=\begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}$$

If $$\begin{pmatrix} 2 & 3 \\ 4 & 1 \end{pmatrix}\times \begin{pmatrix} 5 & -2 \\ -3 & 1 \end{pmatrix}=\begin{pmatrix} 1 & -1 \\ 17 & \lambda  \end{pmatrix}$$ then what is $$\lambda $$ equal to?

If the matrix A is such that $$\begin{bmatrix} 1 & 3\\ 0 & 1\end{bmatrix} A=\begin{bmatrix} 1 & 1 \\ 0 & -1\end{bmatrix}$$, then what is equal to A?

If matrix $$A=\begin{bmatrix} 1 & 2 \\ 4 & 3 \end{bmatrix}$$ such that $$Ax=I$$, then $$x=$$................

If $$[1\,x\,1]  \begin{bmatrix} 1&3&2 \\ 0&5&1\\0&2&0 \end{bmatrix}$$ $$\begin{bmatrix} 1 \\ 1 \\ x \end{bmatrix}=0$$, then the values of $$x$$ are:

The matrix $$A = \begin{bmatrix} 0& 1 & -1\\ -1 & 0 & 1\\ 1 & -1 & 0\end{bmatrix}$$ is a :

If $$\begin{bmatrix} 3 & -1 \\ 0 & 6 \end{bmatrix}\begin{bmatrix} 3x \\ 1 \end{bmatrix}+\begin{bmatrix} -2x \\ 3 \end{bmatrix}=\begin{bmatrix} 8 \\ 9 \end{bmatrix}$$, then the value of $$x$$ is

If $$A=\begin{bmatrix}1&1&-1\\2&-3&4\\3&-2&3\end{bmatrix}$$ and $$B=\begin{bmatrix}-1&-2&-1\\6&12&6\\5&10&5\end{bmatrix}$$, then which of the following is/are correct?
1. A and B commute.
2. AB is null matrix.
Select the correct answer using the code given below :