Let A be an n × n matrix. Is it possible for A2+I = O in the case where n is odd? Answer the same question in the case where n is even.

Can a matrix whose entry is 0 on the diagonal be solved? Explain why or why not. What would you do to remedy the situation?

Let A be an nn matrix in which the entries of each row sum to zero. Find |A|.

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.

Solve for x,y,z and w in the matrix equation wxyx=-432-1+2ywzx.

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.

Is there only one correct method of using row operations on a matrix? Try to explain two different row operations possible to solve the augmented matrix [9312|06] .

Can we add any two matrices together? If so, explain why; if not, explain why not and give an example of two matrices that cannot be added together.