If A is a square matrix, then $(A^T - A)$ is-

For what values of $\lambda$ and $\mu$, the following system of linear equations:

$x+y+2z=1, 2x+y-z=4, x+2y+\lambda z=\mu$

have infinitely many solution?

The following system of equations $2x - y + 3z = 5, 3x + 2y - z = 7, 4x + 5y - \lambda z = \mu$ is consistent. Then

Match List-I with List-II

Let $A$ be any invertible square matrix. Then

Choose the correct answer from the options given below:

If $A$ and $B$ are matrices of the same order, then $AB^T - BA^T$ is a

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

(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 :

Which of the given values of $x$ and $y$ make the following pair of matrices equal ?

$\begin{bmatrix}2x-1 & 4\\y-1 & 3+2x\end{bmatrix}$ and $\begin{bmatrix}0 & y-2\\5 & 4\end{bmatrix}$