Classify the following statements as true or false: I- The determinant of a matrix is equal to the product of the elements of its main diagonal. ...

Classify the following statements as true or false:
I- The determinant of a matrix is equal to the product of the elements of its main diagonal.
II- A system of linear equations is classified as possible and determined if it has at least one solution.
III- The inverse matrix of a matrix A is denoted by A-1 and has the property that A.A-1 = I.
IV- The sum of two matrices is only possible if they have the same order.
V- A symmetric matrix is equal to its transpose.
VI- The determinant of a matrix is always equal to zero if it has a row or column of zeros.
VII- The product of two matrices is only possible if the number of columns of the first matrix is equal to the number of rows of the second matrix.
VIII- A matrix is invertible if and only if its determinant is different from zero.
IX- The solution of a homogeneous system of linear equations is always the null solution.
X- The Cramer's rule can be used to solve a system of linear equations with any number of variables.

I- True
II- True
III- True
IV- True
V- True
VI- True
VII- True
VIII- True
IX- True
X- True