`(AB)^(-1)` = `B^(-1)A ^(-1)` where A and B are invertible matrices satisfying commutative property with respect to multiplication. Write true or false.

If A and B are two invertible matrices of the same order, then adj (AB) is equal to -

If A and B are two invertible matrices of the same order, then adj (AB) is equal to

For two events A and B, P(A) or le P(A). (write true or false)

A and B arer two matrices of order 3xx3 which satisfy AB = A and BA = B. Which of the following are true?

If A and B ar square matrices of the same order and AB=3I , =then A^(-1) is equal to

If A and B are symmetric matrices of the same order, then show that AB is symmetric if and only if A and B commute i.e AB = BA .

Let A={1,omega,omega^(2)} be the set of cube roots of unity. Prepare the composition table for multiplication (xx) on A. Show that multiplication on A is a binary operation and it is commutative on A. Find the identity element for multiplication and show that every element of A is invertible.

If A and B are two square matrices of order 3xx3 which satify AB=A and BA=B , then Which of the following is true ?

If A and B are two non-singular matrices which commute, then (A(A+B)^(-1)B)^(-1)(AB)=

If the matrix [(a,b),(c,d)] is commutative with the matrix [(1,1),(0,1)] then