Proof on matrices :(

massmatics

I need help on proving the proof questions..
1. Let A be an n x n matrix in reduced row echelon form. If A is not equal to In (identity matrix), prove that A has a row consisting entirely of zeros.

2. If A = [a b which is a 2 x 2 matrix;
c d]
show that A is nonsingular if and only if ad-bc is not equal to zero
- So far I know that if the determinant is not equal to zero, then the inverse of A exists. I am stuck on the next step..

3. Find all values of a for which the inverse of the matrix exists. What is A inverse?
A= (1 1 0 ; 3 x 3 matrix
1 0 0
1 2 a)

Plato

MHF Helper
I need help on proving the proof questions..
1. Let A be an n x n matrix in reduced row echelon form. If A is not equal to In (identity matrix), prove that A has a row consisting entirely of zeros.
2. If A = [a b which is a 2 x 2 matrix;
c d]
show that A is nonsingular if and only if ad-bc is not equal to zero
- So far I know that if the determinant is not equal to zero, then the inverse of A exists. I am stuck on the next step..

3. Find all values of a for which the inverse of the matrix exists. What is A inverse?
A= (1 1 0 ; 3 x 3 matrix
1 0 0
1 2 a)

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