If A and B are two invertible matrices, then which of the following statements are correct? (A) $|A^{-1}| = |A|^{-1}$ (B) $adjA = |A|A^{-1}$ (C) $(AB)^{-1} = A^{-1}B^{-1}$ (D) $(A + B)^{-1} = A^{-1} + B^{-1}$ Choose the **correct** answer from the options given below:

Read the following statements carefully:

A. Determinant is a square matrix

B. If A be any given square matrix of order n, then $A(\text{adj}A) = (\text{adj}A)A = |A|I$.

C. If A and B are nonsingular matrices of the same order, then AB and BA are also nonsingular matrices of the same order.

D. If A is a nonsingular matrix, then its inverse does not exist

Which of the above statements are true?

Choose the correct answer from the options given below:

Which of the following statements is (are) true?

(A) $B^T AB$ is a skew-symmetric matrix if A is a symmetric matrix

(B) $B^T AB$ is a symmetric matrix if A is a symmetric matrix

(C) $B^T AB$ is a symmetric matrix if A is a skew-symmetric matrix

(D) $B^T AB$ is a skew-symmetric matrix if B is a skew-symmetric matrix

(E) $B^T AB$ is a symmetric matrix if B is a symmetric matrix

Choose the correct answer from the options given below:

If A is a $2 \times 3$ matrix and B is a matrix such that $A^{T}B$ and $BA^{T}$ are both defined. Then order of B is

If $\begin{vmatrix}6 & 7\\ 3 & 8\end{vmatrix} = \begin{vmatrix}3x & 6\\ -1 & x\end{vmatrix}$, then the sum of values of $x$ is equal

If A is a square matrix of order 3 such that $|A|=2$, then the value of $|adj(adj A)|$ is :

If $A = \begin{bmatrix}0 & a & 1\\-1 & b & 1\\-1 & c & 0\end{bmatrix}$ is a skew symmetric matrix, then the value of $(a+b-c)^2$ is