Q1 of 307 Page 6

If A is an m × n matrix and B is n × p matrix does AB exist? If yes, write its order.

Given: A = m × n matrix and B = n × p matrix

∴ the product AB is defined and the size of the product matrix AB is m × p.

Express the matrix as the sum of a symmetric and a skew-symmetric matrix.

Express the matrix as the sum of a symmetric and skew-symmetric matrix and verify your result.

If and . Write the order of AB and BA.

If and , write AB.