If A is a square matrix of order 3 such that the value of \(|adj\cdot A|=8,\) then the value of \(|A^{T}|\) is:

On the inauguration day of a new showroom, a lucky draw was organized and some vouchers of ₹ 1,000 and 500 were given to the lucky draw winners. A total of 60 vouchers were given on the day. The number of ₹ 1,000 vouchers added to 3 times the number of 500 vouchers, gives 100. Express the given information as a system of linear equations in two variables. Hence, find the number of vouchers of each type by matrix method.

If \[ A = \begin{bmatrix} -1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}, \] then \(A^{-1}\) is

If A=[(1, 0), (2, 1)], B=[(x, 0), (1, 1)] and A=B², then x equals

If A and B are square matrices of order m such that \(A^{2}-B^{2}=(A-B)(A+B),\) then which of the following is always correct?