Matrices Test -...

If $$A=\begin{bmatrix} 2 & -1\\ -7 & 4\end{bmatrix}$$ and $$B=\begin{bmatrix} 4 & 1\\ 7 & 2\end{bmatrix}$$ then $$B^TA^T$$ is equal to?

If $$A^2-A+1=0$$, then the inverse of A is?

Let $$\begin{bmatrix} 1 & 1\\ 0 & 1\end{bmatrix} \begin{bmatrix} 1 & 2\\ 0 & 1\end{bmatrix} \begin{bmatrix} 1 & 3\\ 0 & 1\end{bmatrix}.\begin{bmatrix} 1 & n-1\\ 0 & 1\end{bmatrix}=\begin{bmatrix} 1 & 78\\ 0 & 1\end{bmatrix}$$
If $$A=\begin{bmatrix} 1 & n\\ 0 & 1\end{bmatrix}$$ then $$A^{-1}=?$$

If $$\begin{bmatrix} 1 & 1\\ -1 & 1\end{bmatrix}\begin{bmatrix} x \\ y\end{bmatrix}=\begin{bmatrix} 2 \\ 4\end{bmatrix}$$, then the values of $$x $$ and $$y $$ respectively are?

If $$\begin{bmatrix} 1 & 1\\ 0 & 1\end{bmatrix} \begin{bmatrix} 1 & 2\\ 0 & 1\end{bmatrix}\begin{bmatrix} 1 & 3\\ 0 & 1\end{bmatrix} ..\begin{bmatrix} 1 & n-1\\ 0 & 1\end{bmatrix} =\begin{bmatrix} 1 & 78\\ 0 & 1\end{bmatrix}$$, then the inverse of $$\begin{bmatrix} 1 & n\\ 0 & 1\end{bmatrix}$$ is?

If $$A = \begin{bmatrix} n& 0 & 0\\ 0 & n & 0\\ 0 & 0 & n\end{bmatrix}$$ and $$B = \begin{bmatrix}a_{1} & a_{2} & a_{3}\\ b_{1} & b_{2} & b_{3}\\ c_{1} & c_{2} & c_{3}\end{bmatrix}$$, then $$AB$$ is equal to

If $$A = \begin{bmatrix}1 & 2 & x\\ 0 & 1 & 0\\ 0 & 0 & 1\end{bmatrix}$$ and $$B = \begin{bmatrix}1 & -2 & y\\ 0 & 1 & 0\\ 0 & 0 & 1\end{bmatrix}$$ and $$AB = I_{3}$$, then $$x + y=$$ _____.

If $$A = \begin{bmatrix}1 & 0 & 0\\ 0 & 1 & 0\\ a & b & -1\end{bmatrix}$$, then $$A^{2}$$ is equal to

If $$A = \begin{bmatrix}3 &-4 \\ -1 & 2\end{bmatrix}$$ and $$B$$ is a square matrix of order $$2$$ such that $$AB = I$$ then $$B = ?$$

If $$ \begin{bmatrix} 2 & 1 \\ 3 & 2 \end{bmatrix}A\begin{bmatrix} -3 & 2 \\ 5 & -3 \end{bmatrix}=\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}  $$ , then A =