Let A and B be 3×3 matrices such that $A \neq B$. If $A^3 = B^3$ and $A^2B = B^2A$, then the determinant of $A^2 + B^2$ is:

If $\begin{vmatrix} -1 & a & a^2 \\ -1 & b & b^2 \\ -1 & c & c^2 \end{vmatrix}^2 = \lambda$ and $a - b = 1$, $b - c = 2$ and $c - a = 3$, then the value of $\lambda$ is

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

For any 3 ×3 matrix $A$, if $A(adj\,A) = \begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix}$, then $2|A|$ is equal to

If $A = \begin{bmatrix}1 & 2\\3 & 4\end{bmatrix}$ such that $A^2 + \beta A + \gamma I = 0$ then $\beta + \gamma$ is equal to:

(where $I$ is an identity matrix of order 2)

If $A^2 - A + I = O$, where O is the zero matrix and I is the identity matrix, then $A^{-1}$ is

If $A$ is an invertible matrix of order 3, then

Match List-I with List-II

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