matrix groups

Question

Which of the following is true?

• Every lower triangular matrix is group under multiplication operation where all elements of diagonal are non zero numbers.
• Every diagonal matrix is group under multiplication operation, where all elements of diagonal are non zero numbers.
• Every matrix is Abelian under addition operation where all elements are real numbers.
• Both (a) and b)

isn't a b c all are correct?

Comments

All are correct.

Answer 1

Yep. I too think so.

A, B are correct because the matrix is non-singular so it'll have an inverse.

C is correct because for addition even singular matrices will work because the "inverse" of a matrix is simply -1 * matrix.

Answer 2

• 
  • so U can understand not every matrix has inverse----so Not even a group
  • if "Every" Word is not given then the statement may be correct