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Consider the following statements in res...

Consider the following statements in respect of the matrix `A=[{:(0,1,2),(-1,0,-3),(-2,3,0):}]`
1. The matrix A is skew-symmetric.
2. The matrix A is symmetric.
3. The matrix A is invertible.
Which of the above statements is/are correct ?

A

1 only

B

3 only

C

1 and 3

D

2 and 3

Text Solution

Verified by Experts

The correct Answer is:
A
`A=[(0,1,2),(-1,0,-3),(-2,3,0)]`
`A^(T)=[(0,-1,-2),(1,0,3),(2,-3,0)]=-[(0,1,2),(-1,0,-3),(-2,3,0)]=-A`
Hence, A is skew symmetric matrix
`|A|=|(0,1,2),(-1,0,-3),(-2,3,0)|=1(-6)-2(-3)=-6+6=0`
Therefore A is non-invertible.
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