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 order n , then prove that A \ a n d \ B will commute iff A-lambdaI \ a n d \ B-lambdaI commute for every scalar lambda .

If A and B are square matrices of order n , then prove that A and B will commute iff A-lambda\ I and B-lambda\ I commute for every scalar lambda

If A is a square matrix of order n , prove that |Aa d jA|=|A|^n

Let A and B are two matrices such that AB = BA, then for every n in N

If A and B are commuting square matrices of the same order, then which of the following is/are correct ?

If A and B are two square matrices such that they commute, then which of the following is true?

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, that is A B = B A .

If A and B are square matrices of the same order such that A B = B A , then proveby induction that A B^n=B^n A . Further, prove that (A B)^n=A^n B^n for all n in N .

If Aa n dB are symmetric matrices of the same order, write whether AB-BA is symmetric or skew-symmetric or neither of the two.