(solution) prove that set M(mn) of all m*n matrices with their element as

(solution) prove that set M(mn) of all m*n matrices with their element as

prove that set  M(mn) of all m*n matrices  with their element as rational number is not a vector space over the field R of real number

Let M be the set of all m n matrices with rational numbers
as their elements.
Let ¡ be the field of real numbers.
Consider the irrational number r.
Consider a matrix P M
Now the elements of matrix…