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 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

If A and B are square matrices of order n, then A - lambda I and B - lambda I commute for every scalar lambda only if a)AB = BA b) AB + BA = 0 c)A = - B d)None of these

A and Bare square matrices of order n.Their product is commutative:Prove that A^2B = BA^2 .

If A and B are square matrices of the same order such that A B = B A , then prove by induction that A B^n=B^n A .