Question 1046201: I need help to show a 2x2 matrix is invertible by using A has n pivot positions.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Matrix A has two pivots on the main diagonal, that is, being one down and one right from the one before it.
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1) This implies that the reduced echelon form of A is I2 - the identity matrix
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2) This means that if A has two pivots, then A is equivalent to the 2 by 2 identity matrix
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Also 2) implies that A is invertable because
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" an n x n matrix, called A is invertible iff (if and only if) A is row equivalent to In , and any sequence of elementary row operations that reduces A to In also transforms In into A-1"
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