If M and N are square matrices of order 3 such that det \((M)=m\) and \(MN=mI,\) then det (N) is equal to:

Let both \(AB^{\prime}\) and \(B^{\prime}A\) be defined for matrices A and B. If order of A is \(n\times m\), then the order of B is:

If |(a, 3, 4), (1, 2, 1), (1, 4, 1)| = 0, then the value of a is

If |A|=2, where A is a $2\times2$ matrix, then |4$A^{-1}$| equals :

A furniture workshop produces three types of furniture chairs, tables and beds each day. On a particular day the total number of furniture pieces produced is 45. It was also found that production of beds exceeds that of chairs by 8, while the total production of beds and chairs together is twice the production of tables. Determine the units produced of each type of furniture, using matrix method.