If A, B, and C are three square matrices of the same order, then `AB=AC implies B=C`. Then

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

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

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

If A and B are two nonzero square matrices of the same order such that the product AB=O , then

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

A, B and C are three square matrices of order 3 such that A= diag. (x, y, x), det. (B)=4 and det. (C)=2 , where x, y, z in I^(+) . If det. (adj. (adj. (ABC))) =2^(16)xx3^(8)xx7^(4) , then the number of distinct possible matrices A is ________ .

If A , B are two square matrices of same order such that A+B=AB and I is identity matrix of order same as that of A , B , then

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

Let A and B be square matrices of the same order such that A^(2)=I and B^(2)=I , then which of the following is CORRECT ?

If A, B and C are invertible matrices of some order, then which one of the following is not true?