If $A = \begin{bmatrix} -2 & 2 \\ -3 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$, then $(B^{-1} A^{-1})^{-1}$ is equal to
- A$\begin{bmatrix} 2 & 2 \\ 2 & 3 \end{bmatrix}$
- B$\begin{bmatrix} 3 & -2 \\ 2 & 2 \end{bmatrix}$
- C$\frac{1}{10} \begin{bmatrix} 2 & 2 \\ -2 & 3 \end{bmatrix}$
- D$\frac{1}{10} \begin{bmatrix} 3 & 2 \\ -2 & 2 \end{bmatrix}$
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Suppose $A$ is any $3 \times 3$ non-singular matrix and $(A-3 I)(A-5 I)=O$,where $I=I_3$ and $O=O_3$. Here $O_3$ represents the zero matrix of order $3$ and $I_3$ is the identity matrix of order $3$. If $\alpha A+\beta A^{-1}=4 I$,then $\alpha+\beta$ is equal to:
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Medium
View SolutionIf $A$ is a square matrix of order $n$,$|A| = D$,and $|adj(A)| = D'$,then:
Easy
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