Question

Find the inverse of the given matrix by elementary transformation (3x3 matrix)
[0 1 2]
A= |1 2 3|
[3 1 3]

Answer 1

A=[ 32107 ]

We know that A=IA (using row operations)

[ 32 107 ]=[ 1001 ]A

Using operation R 1

⇒R 1 −R 2

[ 1237 ]=[ 10−11 ]A

Using operation R 2

⇒R 2 −2R 1

[ 1031 ]=[ 1−2−13 ]A

Using operation R 1

⇒R 1 −3R 2

[ 1001 ]=[ 7−2−103 ]A

Therefore,

A −1 =[ 7−2−103 ]

Answer 2

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