Let A be a 3 × 3 matrix satisfying A3 - 5A2 + 7A + I = 0. If A5 - 6A4 + 12A3 - 6A2 + 2A + 2I = lA + mI, then find the value of l + m.

Let T2 be the set of all 2 × 2 matrices A = a bc d where a, b, c, d ∈ {0, 1, 2, 3, 4, 5, 6}. Find the number of matrices A such that A is either symmetric or skew-symmetric and det(A) is divisible by 7.

If f(x) = [cos x -sin x 0; sin x cos x 0; 0 0 1], then f(x + y) is equal to:

If A = 13 [1 -2 2; -2 1 2; -2 -2 -1], then matrix A is: