Consider the set of matrices 0 S = {(a+b):abER} a, bЄR (a) Prove that S is a subring of the ring M2×2 (R). b) State which axioms of a field are satisfied by the subring S. You are not required. to prove anything.

Determine if the statement is true or false. If the statement is false, then correct it and make it true. For the product of two matrices to be defined, the number of rows of the first matrix must equal the number of columns of the second matrix.

Can you explain whether a 2×2 matrix with an entire row of zeros can have an inverse?

Use an example chosen from 22 matrices to show that for nn matrices A and B,ABBA but AB=BA.

Determine if the statement is true or false. If the statement is false, then correct it and make it true. A 75 matrix has 5 rows.

Find the sequence of the elementary matrices whose product is the non singular matrix below. [2410]

We can add (or subtract) two matrices only if they have the same ______.

Show that no 22 matrices A and B exist that satisfy the matrix equation. AB-BA=1001.