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Question

Let A=001010100. The only correct statement about the matrix A is
  1. A2=I
  2. A is a zero matrix
  3. A1 does not exist.
  4. A = (-1)I, where I is a unit matrix.


Solution

The correct option is A A2=I
The given matrix is A=001010100
It is clear that A is not a zero matrix.
I=1 100010001 Ai.e.,(1)IA|A|=0[1000]0[0010]1[0110]=001(1)=1Since|A|0,A1exists.A2=A.A=001010100001010100=100010001=I

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