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

D_(1) is always equal to

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. (|A|+K)^(n-2) b. (|A|+K)^n c. (|A|+K)^(n-1) d. none of these

If A is an orthogonal matrix then A^(-1) equals a. A^T b. A c. A^2 d. none of these

If for the matrix A ,\ A^3=I , then A^(-1)= (a) A^2 (b) A^3 (c) A (d) none of these

If A^3 =O, then I+ A + A^2 = (where I is the unit matrix of order same as that of square matrix A) is equals (A) I -A (B) (I-A)^-1 (C) (I+A) (D) none of these

(A^(3))^(-1)=(A^(-1))^(3) , where A is a square matrix and |A|!=0

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

A square matrix A is invertible if det(A) is equal to (A) -1 (B) 0 (C) 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 an invertible matrix then det(A^-1) is equal to (A) 1 (B) 1/|A| (C) |A| (D) none of these