Consider the following in respect of matrices A, B and C of same order :
1. `(A+B+C)'=A'+B'+C'`
2. `(AB)'=AB'`
3. `(ABC)'=C'B'A'`
Where A' is the transpose of the matrix A. Which of the above are correct ?

Consider the following in respect of matrices A,B and C of same order. I. (A+B+C)=A+B+C II. (AB)'=B'A' III. (ABC) =C'B'A Where A' is the transpose of the matrix A. Which of the above are correct ?

Consider the following in respect of natural numbers a, b and c: 1. LCM (ab, ac) = a LCM(b, c) 2. HCF(ab, ac) = a HCF(b, c) 3. HCF (a, b) lt LCM (a, b) 4. HCF (a, b) divides LCM(a, b). Which of the above are correct?

AB=ACimplies B=C for any three matrices of same order .

State with reason, whether the following are true of false. A, B and C are matrices of order 2 xx 2 . A.(B-C)=A.B-A.C

Consider the following statements in respect of symmetric matrices A and B 1. AB is symmetric. 2. A^(2) + B^(2) is symmetric. Which of the above statement(s) is/are correct ?

If A,B,C are non - singular matrices of same order then (AB^(-1)C)^(-1)=

if A and B are square matrices of same order such that A = and B = B, where A denotes the conjugate transpose of A, then (AB-BA)* is equal to

if A and B are square matrices of same order such that A*=A and B* = B, where A* denotes the conjugate transpose of A, then (AB-BA)* is equal to

if A and B are square matrices of same order such that A*=A and B* = B, where A* denotes the conjugate transpose of A, then (AB-BA)* is equal to

if A and B are square matrices of same order such that A*=A and B* = B, where A* denotes the conjugate transpose of A, then (AB-BA)* is equal to