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 A=x % of y a n d B=y % of x , t h e n which of the following is true? a.A is smaller than B b.A is greater than B. c.Relationship between A and B cannot be determined d.If x is smaller than y, then A is greater than B e.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? B^T A B is symmetric matrix if A is symmetric B^T A B is symmetric matrix if B is symmetric B^T A B is skew-symmetric matrix for every matrix A B^T A B is skew-symmetric matrix if A is skew-symmetric

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

If A,B and A+B are idempotent matrices, 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? C D=(60sqrt(2))/(17) (b) B D=(65)/(17) A D=(60sqrt(2))/(17) (d) none of these

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

Let a = b (mod n), a'= b' (mod n) and d, m in N. Then which of the following need not be true?