List of top Mathematics Questions on Product of Matrices asked in CUET (UG)

If \( A = \begin{bmatrix} \cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha \end{bmatrix} \) then \( A^2 - (2 \cos \alpha) A \) is equal to: (Where I is identity matrix of order 2)

If A, B and C are square matrices of order n x n, then which of the following are TRUE? [Where $A^T$ is transpose of matrix A]
(A) \( (A + B)^T = A^T + B^T \)
(B) \( (AB)^T = A^T B^T \)
(C) \( (ABC)^T = C^T B^T A^T \)
(D) \( (BA)^T = A^T B^T \)
Choose the correct answer:

If $A=\begin{bmatrix} a & b \\ b & a \end{bmatrix}$ and $A^{2}=\begin{bmatrix} \alpha & \beta \\ \beta & a \end{bmatrix}$, then $(a-b)$ is:

Match List-I (Matrix expressions) with List-II (Properties).