- #1
johncena
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Q:Prove that a square matrix A is invertible iff A is non singular.
My Ans: Since the inverse of a square matrix is given by,
A^ = (1/|A|)adj.A (Where A^ is A inverse)
If |A|=0, A^ is not defined.
i.e, A^ exist only if A is non singular. In other words, a square matrix A is invertible iff A is non singular.
Conversly, Let |A|=0, i.e., let A be singular.
then, A^=(1/|A|)adj.A = (1/0)adj.A (not defined)
Hence we conclude that A^ exist only if A is non singular.
I got only 1 out of 5 marks for this answer. What is missing in my answer?
My Ans: Since the inverse of a square matrix is given by,
A^ = (1/|A|)adj.A (Where A^ is A inverse)
If |A|=0, A^ is not defined.
i.e, A^ exist only if A is non singular. In other words, a square matrix A is invertible iff A is non singular.
Conversly, Let |A|=0, i.e., let A be singular.
then, A^=(1/|A|)adj.A = (1/0)adj.A (not defined)
Hence we conclude that A^ exist only if A is non singular.
I got only 1 out of 5 marks for this answer. What is missing in my answer?