Find the inverse matrix of $\begin{bmatrix} 4 & 7 \\ 1 & 2 \end{bmatrix}$.

Find $P^{-1},$ if it exists,given $P=\left[\begin{array}{cc}10 & -2 \\ -5 & 1\end{array}\right].$

If $A = \begin{bmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \end{bmatrix}$, then which of the following is true?

Which of the following statements is incorrect for a square matrix $A$ where $|A| \neq 0$?

Let $A = \begin{bmatrix} 1 & 2 \\ -1 & 4 \end{bmatrix}$. If $A^{-1} = \alpha I + \beta A$,where $\alpha, \beta \in \mathbb{R}$ and $I$ is a $2 \times 2$ identity matrix,then $4(\alpha - \beta)$ is equal to:

Consider the matrices $A = \begin{bmatrix} 2 & -2 \\ 4 & -2 \end{bmatrix}$ and $B = \begin{bmatrix} 3 & 9 \\ 1 & 3 \end{bmatrix}$. If matrices $P$ and $Q$ are such that $PA = B$ and $AQ = B$, then the absolute value of the sum of the diagonal elements of $2(P+Q)$ is . . . . . . .