If $A=\begin{bmatrix}5 & 0 & 0\\0 & 5 & 0\\0 & 0 & 5\end{bmatrix}$ such that $A^5=\lambda^2 A$, then the value of $\lambda$ is

If $x, y$ and $z$ are non-zero distinct numbers, then $\begin{vmatrix} x+y & y+z & z+x \\ z & x & y \\ 1 & 1 & 1 \end{vmatrix}$ is equal to

For any non-zero matrix $A = [a_{ij}]_{3\times3}$ and $|A| \neq 0$, then

Match the LIST-I with LIST-II

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If the area of a triangle with vertices $(-3,0)$, $(3, 0)$ and $(0, k)$ is 9 sq. units, then k equals

If A and B are square matrices of order n, such that AB = A and BA = B, then $A^2$ =

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

(A) AB - BA is a skew symmetric matrix

(B) AB is a symmetric matrix

(C) AB is a scalar matrix

(D) AB + BA is a symmetric matrix

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If $P = \begin{bmatrix} 1 & 2 \\ -1 & 3 \end{bmatrix}$, $Q = \begin{bmatrix} 4 & 0 \\ 1 & 5 \end{bmatrix}$ and $R = \begin{bmatrix} 2 & 0 \\ 1 & -2 \end{bmatrix}$, then which of the following are TRUE?

(A) $(P^T)^T = P^T$

(B) $(P-Q)R = PR - QR$

(C) $(P-Q)^T = Q^T - P^T$

(D) $(PQ)^T = Q^TP^T$

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