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

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

If positive quantities a,b,c are in H.P. , then which of the following is not true ? a. b gt (a+c)/(2) b. (1)/(a-b)-(1)/(b-c) gt 0 c. ac gt b^(2) d. none of these

A matrix A is said to be an Idempotent matrix if A^2=A . Then which of the following is true

Let Aa n dB be two nonsingular square matrices, A^T a n dB^T are the transpose matrices of Aa n dB , respectively, then which of the following options are correct? (correct option may be more than one) (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

Which of the following is mechanical tissue? a. Xylem fibre b. Phloem fibre c. a & b d. None of the these.

If ( vec axx vec b)xx( vec cxx vec d) . ( vec axx vec d)=0 , then which of the following may be true? (a) 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 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

A square matrix A is used to be an idempotent matrix if A^(2) = A . If A is an idempotent matrix and B = I -A, then-

In A B C ,a=5,b=12 ,c=90^0a n dD is a point on A B so that /_B C D=45^0dot Then which of the following is not true? (a) C D=(60sqrt(2))/(17) (b) B D=(65)/(17) (c) A D=(60sqrt(2))/(17) (d) none of these