List of top Mathematics Questions on Matrices asked in PSEB XII

Ajay, Sameer and Meenal have Rs. 20/- each and some footballs, basketballs and volleyballs in their shops. In a week, Ajay sold 3 footballs and a volleyball but he bought 2 basketballs for his shop and he has Rs. 35/- now. In same duration, Sameer sold 2 basketballs and 2 volleyballs but he bought a football for his shop and he has Rs. 95/- now. Similarly, Meenal sold 2 footballs and a basketball but she bought 3 volleyballs for her shop and she has Rs. 15/- now. Find the cost of a football, a basketball and a volleyball by the help of matrices.
If \( X = \begin{bmatrix} 3 & 1 \\ 2 & -1 \end{bmatrix} \) and \( 2X - Y = \begin{bmatrix} 5 & 10 \\ 3 & -5 \end{bmatrix} \), then find the matrix \( Y \).
If \( A = \begin{bmatrix} 2 & 1 & 3 \\ 4 & 1 & 0 \end{bmatrix} \), \( B = \begin{bmatrix} 1 & -1 \\ 0 & 2 \\ 5 & 0 \end{bmatrix} \) then verify that \( (AB)' = B'A' \)

If 

then \( y \) is equal to: 
 

If the order of the matrix \( A \) is \( 3 \times 2 \), then the order of the matrix \( (A')' \) is: