For a 2 × 2 matrix A = [ ], whose elements are given by , write the value of .


Let R be the equivalence relation in the set A = {0, 1, 2, 3, 4, 5} given by R = {(a, b) : 2 divides (a –b)}. Write the equivalence class [0].
If m and n are the order and degree, respectively of the differential equation = sin x, then write the value of m + n.
If a line has direction ratios 2, – 1, – 2, then what are its direction cosines ?
If A is a square matrix such that A² = A, then write the value of (I + A)² – 3A.