Question 1: If A and B are square matrices of same order such that \(AB=A\) and \(BA=B\), then \(A^{2}+B^{2}\) is equal to:

• A. \(A+B\)
• B. \(BA\)
• C. \(2(A+B)\)
• D. \(2BA\)

Question 2: The matrix \([\begin{bmatrix}0&1&-2\\ -1&0&-7\\ 2&7&0\end{bmatrix}]\) is a:

• A. diagonal matrix
• B. symmetric matrix
• C. skew symmetric matrix
• D. scalar matrix

Question 3: If \(A=\begin{bmatrix}5&0&0\\ 0&5&0\\ 0&0&5\end{bmatrix},\) then \(A^{3}\) is:

• A. \(3\begin{bmatrix}5&0&0\\ 0&5&0\\ 0&0&5\end{bmatrix}\)
• B. \(\begin{bmatrix}125&0&0\\ 0&125&0\\ 0&0&125\end{bmatrix}\)
• C. \(\begin{bmatrix}15&0&0\\ 0&15&0\\ 0&0&15\end{bmatrix}\)
• D. \(\begin{bmatrix}5^{3}&0&0\\ 0&5&0\\ 0&0&5\end{bmatrix}\)

Question 4: A school wants to allocate students into three clubs: Sports, Music and Drama, under following conditions:

• The number of students in Sports club should be equal to the sum of the number of students in Music and Drama club.

• The number of students in Music club should be 20 more than half the number of students in Sports club.}

• The total number of students to be allocated in all three clubs are 180.

Find the number of students allocated to different clubs, using matrix method.