List of top Mathematics Questions on Matrices asked in CBSE CLASS XII

If \[ P = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{bmatrix} \quad \text{and} \quad Q = \begin{bmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 1 & -1 & 5 \end{bmatrix} \] find \( QP \) and hence solve the following system of equations using matrix method:
\[ x - y = 3,\quad 2x + 3y + 4z = 13,\quad y + 2z = 7 \]

If \[ A = \begin{bmatrix} \frac{1}{2}\cos x & -\sin x \\ \sin x & \frac{1}{2}\cos x \end{bmatrix} \] and \(A + A^T = I\), then the value of \(x \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\) is

If $A$ and $B$ are square matrices of same order, then which of the following statements is/are always true?
(i) $(A+B)(A-B)=A^2-B^2$
(ii) $AB=BA$
(iii) $(A+B)^2=A^2+AB+BA+B^2$
(iv) $AB=0 \Rightarrow A=0$ or $B=0$