The matrix $X$ in the equation $AX = B$, such that $A = \begin{bmatrix} 1 & 3 \\ 0 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & -1 \\ 0 & 2 \end{bmatrix}$ is given by

The value of $\Delta = \begin{vmatrix} 2\sin40^\circ & 2\sin50^\circ \\ -3\cos40^\circ & 3\cos50^\circ \end{vmatrix}$ is:

The value of $\begin{vmatrix} 1 & a & b+c \\ 1 & b & c+a \\ 1 & c & a+b \end{vmatrix}$ is

If $A = \begin{bmatrix} 9 & 7 & 5 \\ 6 & 4 & 2 \\ 1 & 3 & 8 \end{bmatrix}$, then (cofactor of $a_{13}$ - cofactor of $a_{32}$ )will be equal to :

If $A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 2 & 3 & -1 \end{bmatrix}$, then $A^2$ is equal to

Let A be a square matrix of order 3 such that $|A|=3$, then the value of $\frac{|adj(adjA)|}{|A|}$ is

If P and Q are symmetric matrices, then QP-PQ is