`(-A)^(-1)` is always equal to (where `A` is nth-order square matrix) `(-A)^(-1)` b. `-A^(-1)` c. `(-1)^nA^(-1)` d. none of these

If A^3=O ,t h e nI+A+A^2 equals a. I-A b. (I+A^1)^(-1) c. (I-A)^(-1) d. none of these

If Aa n dB are symmetric and commute, then which of the following is/are symmetric? A^(-1)B b. A B^(-1) c. A^(-1)B^(-1) d. none of these

Let A be an nth-order square matrix and B be its adjoint, then |A B+K I_n| is (where K is a scalar quantity) (|A|+K)^(n-2) b. (|A|+)K^n c. (|A|+K)^(n-1) d. none of these

The value of lim_(m->oo)(cos(x/m))^("m") is 1 (b) e (c) e^(-1) (d) none of these

The value of sum_(r=1)^(n+1)(sum_(k=1)^n "^k C_(r-1)) ( where r ,k ,n in N) is equal to a. 2^(n+1)-2 b. 2^(n+1)-1 c. 2^(n+1) d. none of these

If A is order 2 square matrix such that |A|=2, then |(adj(adj(adjA)))| is 512 b. 256 c. 64 d. none of these

The value of 2tan^(-1)(cos e ctan^(-1)x-tancot^(-1)x) is equal to (a) cot^(-1)x (b) cot^(-1)1/x (c) tan^(-1)x (d) none of these

The value of the determinant of n^(t h) order, being given by |x1 11x11 1x | is (x-1)^(n-1)(x+n-1) b. (x-1)^n(x+n-1) c. (1-x)^(-1)(x+n-1) d. none of these

If P is an orthogonal matrix and Q=P A P^T an dx=P^T Q^1000 P then x^(-1) is , where A is involutary matrix. A b. I c. A^(1000) d. none of these

The ends of a diagonal of a square are (2,-3) and (-1,1)dot Another vertex of the square can be a. (-3/2,-5/2) (b) (5/2,1/2) (1/2,5/2) (d) none of these