If `A B=Aa n dB A=B ,` then which of the following is/are true? `A` is idempotent b. `B` is idempotent c. `A^T` is idempotent d. none of these

In which of the following type of matrix inverse does not exist always? a. idempotent b. orthogonal c. involuntary d. none of these

In which of the following type of matrix inverse does not exist always? a. idempotent b. orthogonal c. involuntary 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

For any two sets Aa n dB which of the following is pair wise disjoint family of sets AnnB , A-B , AuuB b. AnnB , B-A , AuuB c. A-B , AnnB , B-A d. none of these

Let Aa n dB be two nonsinular square matrices, A^T a n dB^T are the transpose matrices of Aa n dB , respectively, then which of the following are correct? (a) . B^T A B is symmetric matrix (b) . if A is symmetric B^T A B is symmetric matrix (c) . if B is symmetric B^T A B is skew-symmetric matrix for every matrix A (d) . B^T A B is skew-symmetric matrix if A is skew-symmetric

If a,b,c are in A.P. and a^2,b^2,c^2 are in H.P. then which of the following could and true (A) -a/2, b, c are in G.P. (B) a=b=c (C) a^3,b^3,c^3 are in G.P. (D) none of these

If ( vec axx vec b)xx( vec cxx vec d)dot( vec axx vec d)=0 , then which of the following may be true? vec a , vec b , vec ca n d vec d are necessarily coplanar b. vec a lies in the plane of vec ca n d vec d c. vec b lies in the plane of vec aa n d vec d d. vec c lies in the plane of vec aa n d vec d

If B is an idempotent matrix, and A=I-B , then

If A is an idempotent matrix, then show that B=l-A is also idempotent and AB=BA=0

If Aa n dB are two matrices such that A B=Ba n dB A=A ,t h e n (A^5-B^5)^3=A-B b. (A^5-B^5)^3=A^3-B^3 c. A-B is idempotent d. none of these