If A and B are symmetric matrices of same order, then which of the following statements are true?

(A) $AB^T+B^TA$ is a skew-symmetric matrix.

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

(C) $(AB)^T(A^T)^{-1}=B$

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

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If $A = \begin{bmatrix} 1 & -3 \\ 2 & 0 \end{bmatrix}$, then which of the following statement(s) is/are TRUE?

(A) Matrix A is non-singular

(B) $|3A| = 54$

(C) $|adjA| = 36$

(D) $A^2 = \begin{bmatrix} -5 & -3 \\ 2 & -6 \end{bmatrix}$

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If the points $(2, -3)$, $(\lambda, -1)$ and $(0, 4)$ are collinear, then the value of $\lambda$ is

If $A=\begin{bmatrix}0 & b-a & c-a\\a-b & 0 & c-b\\a-c & b-c & 0\end{bmatrix}$ then the value of $\lvert A \rvert$ is

The linear equation involving $x$ and $y$ are written in matrix form as:

Let P and Q be any two invertible matrices of the same order. Then

Match List-I with List-II

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If a, b and c are all different from zero and $\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix} = 0$, then the value of $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$ is :