If A and B are invertible matrices then which of the following statement is NOT correct?

If $A=\begin{bmatrix}a & 0\\0 & 0\end{bmatrix}$ and $B=\begin{bmatrix}0 & 0\\0 & b\end{bmatrix}$ then the matrix $A^3B^3$ is:

$\Delta=\left|\begin{array}{ccc}1 & \cos x & 1 \\ -\cos x & 1 & \cos x \\ -1 & -\cos x & 1\end{array}\right|$

(A) $\Delta=2\left(1-\cos ^{2} x\right)$

(B) $\Delta=2\left(2-\sin ^{2} x\right)$

(C) Minimum value of $\Delta$ is $2$

(D) Maximum value of $\Delta$ is $4$

Choose the correct answer from the options given below :

If $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$, then the value of $A^{20}$ is:

If $A = [a_{ij}]_{3×3}$ where $a_{ij} = \begin{cases} (-1)^{i+j} - 1, & i = j \\ (-1)^{i+j}, & i \neq j \end{cases}$ then the value of $A + A^T$ is:

If A is a square matrix such that $A^2 = I$, then $(A+I)^3 + (A-I)^3 - 7A$ is equal to

If A is an invertible matrix, then which of the following statement(s) is/are TRUE?

(A) $|A^{-1}| = |A|$

(B) $(A^{-1})^{-1} = A$

(C) $A^{-1} = \frac{adj A}{|A|}$

(D) $(A^T)^{-1} = (A^{-1})^T$

Choose the correct answer from the options given below: