Question

If \(A\) and \(B\) are two matrices such that \(AB\) is defined and \(AB = A\), then \(B\) is:

• A. Identity matrix
• B. Null matrix
• C. Unit matrix
• D. Inverse of \(A\)

Hint:

Identity matrix leaves a matrix unchanged on multiplication.

Answer 1

The Correct Option is A

\[ AB = A \Rightarrow A(B-I)=0 \] For non-zero \(A\), \(B = I\).