If A and B are square matrices of order n, then `A-lambdaI` and `B-lambdaI` commute for every scalar `lambda`, only if

If A is a square matrix of order n, then |adj A|=

If A and B are square matrix of same order then (A-B)^(T) is:

If A and B are symmetric matrices of order n,where (A ne B) ,then:

If A and B are symmetric matrices of same order than AB-BA is a:

If A and B are square matrices of order n , then prove that Aa n dB will commute iff A-lambdaIa n dB-lambdaI commute for every scalar lambdadot

If A and B are square matrices of orders 3 such that |A|=-2 and |B|=3 find the value of |3AB| .

If A and B are square matrices of order 3 such that |A| = -1 and |B| = 3, find the value of |3AB|.

If A and B are square matrices of same order such that AB=O and B ne O , then prove that |A|=0 .