Let $$A = \left( {\matrix{ 1 & 0 & 0 \cr 0 & {\cos t} & {\sin t} \cr 0 & { - \sin t} & {\cos t} \cr } } \right)$$

Let $$\lambda$$₁, $$\lambda$$₂, $$\lambda$$₃ be the roots of $$\det (A - \lambda {I_3}) = 0$$, where I₃ denotes the identity matrix. If $$\lambda$$₁ + $$\lambda$$₂ + $$\lambda$$₃ = $$\sqrt 2 $$ + 1, then the set of possible values of t, $$-$$ $$\pi$$ $$\ge$$ t < $$\pi$$ is

Let A and B two non singular skew symmetric matrices such that AB = BA, then A²B²(A^TB)^$$-$$1(AB^$$-$$1)^T is equal to

If a_n (> 0) be the n^th term of a G.P. then

$$\left| {\matrix{ {\log {a_n}} & {\log {a_{n + 1}}} & {\log {a_{n + 2}}} \cr {\log {a_{n + 3}}} & {\log {a_{n + 4}}} & {\log {a_{n + 5}}} \cr {\log {a_{n + 6}}} & {\log {a_{n + 7}}} & {\log {a_{n + 8}}} \cr } } \right|$$ is equal to

Let T and U be the set of all orthogonal matrices of order 3 over R and the set of all non-singular matrices of order 3 over R respectively. Let A = {$$-$$1, 0, 1}, then