The number of diagonal matrices of order 3 with elements either 1 or 2, is:

The values of $x, y, z$ and $w$ such that $\begin{bmatrix} x-y & 2z+w \\ 2x-y & 2x+w \end{bmatrix} = \begin{bmatrix} 5 & 3 \\ 12 & 15 \end{bmatrix}$ are given by

The value of the determinant $\Delta=\begin{vmatrix}\cos\alpha\cos\beta & \cos\alpha\sin\beta & -\sin\alpha\\-\sin\beta & \cos\beta & 0\\\sin\alpha\cos\beta & \sin\alpha\sin\beta & \cos\alpha\end{vmatrix}$ is:

If $A = \begin{bmatrix} 5 & 2 \\ 4 & 3 \end{bmatrix}$ is a given matrix, then which of the following statements are correct?

(A) $|A| = 7$

(B) minor of $3 = -5$

(C) co-factor of $2 = -4$

(D) $adj(A) = \begin{bmatrix} 3 & -2 \\ -4 & 5 \end{bmatrix}$

Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 2 & 3 \\ 5 & -2 \end{bmatrix}$ be such that $A^{-1} = KA$, then the value of K is:

If A and B are square matrices of order 3×3 such that |A|=7 and |B|=6, then |B adj A| =

If the area of a triangle whose vertices are (-1, 3), (1, -5) and (k, 2) where $k > 0$ is 30 sq. units, then the value of k is