A square matix A is a called singular if det A is (A) negative (B) zero (C) positive (D) non-zero

A square matix A is called idempotent if (A) A^2=0 (B) A^2=I (C) A^2=A (D) 2A=I

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

Each diagonal element of a skew symmetric matrix is (A) zero (B) negative (C) positive (D) non real

Which of the following statement are true? (i) The product of a positive and negative integer is negative. (ii) The product of three negative integers is a negative integer. (iii) Of the two integers, if one is negative, then their product must be positive. (iv) For all non-zero integers a and b , axxb is always greater than either a or b. (v) The product of a negative and a positive integer may be zero. (vi) There does not exist an integer b such that for a gt1, axxb=bxxa=b.

If A,B and C be the three square matrices such that A=B+C then det A is necessarily equal to (A) detB (B) det C (C) det B+detC (D) none of these

If Aa n dB are square matrices of the same order and A is non-singular, then for a positive integer n ,(A^(-1)B A)^n is equal to A^(-n)B^n A^n b. A^n B^n A^(-n) c. A^(-1)B^n A^ d. n(A^(-1)B^A)^

If B is a non-singular matrix and A is a square matrix, then det (B^(-1) AB) is equal to (A) det (A^(-1)) (B) det (B^(-1)) (C) det (A) (D) det (B)

If B is a non-singular matrix and A is a square matrix, then det (B^(-1) AB) is equal to (A) det (A^(-1)) (B) det (B^(-1)) (C) det (A) (D) det (B)

If a ,b ,c are sides of a scalene triangle, then value of |[a, b, c] ,[b, c, a] ,[c, a, b]| is positive (b) negative non-positive (d) non-negative

If A ,\ B are square matrices of order 3,\ A is non-singular and A B=O , then B is a (a) null matrix (b) singular matrix (c) unit matrix (d) non-singular matrix