Consider the following statements:
Statement $I$: If $A$ is a non-singular matrix, then $A^{-1}$ exists.
Statement $II$: If $A$ and $B$ are symmetric matrices of the same order, then $(AB - BA)$ is a skew-symmetric matrix.
Choose the correct option.
Statement $I$: If $A$ is a non-singular matrix, then $A^{-1}$ exists.
Statement $II$: If $A$ and $B$ are symmetric matrices of the same order, then $(AB - BA)$ is a skew-symmetric matrix.
Choose the correct option.
- AStatement $I$ is true and statement $II$ is false
- BStatement $I$ is false and statement $II$ is false
- CStatement $I$ is true and statement $II$ is true
- DStatement $I$ is false and statement $II$ is true
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Let $A=\left[\begin{array}{ccc}1 & -2 & 1 \\ -2 & 3 & 1 \\ 1 & 1 & 5\end{array}\right]$. Verify that $\left(A^{-1}\right)^{-1}=A$.
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If $A = \begin{bmatrix} 5 & 2 \\ 3 & 1 \end{bmatrix}$,then $A^{-1} = $
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If $A = \begin{bmatrix} 1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 0 \end{bmatrix}$ and $A(\operatorname{adj} A) = K I$,then the value of $K$ is (where $I$ is the unit matrix of order $3$).
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