If A and B are two square matrices of order `3xx3` which satify `AB=A` and `BA=B`, then Which of the following is true ?A. If matrix A is singular, then matrix B is nonsingular.B. If matrix A is nonsingular, then materix B is singular.C. If matrix A is singular, then matrix B is also singular.D. Cannot say anything.

If A and B are two square matrices of order `3xx3` which satify `AB=A`

1.	If A and B are two square matrices of order `3xx3` which satify `AB=A` and `BA=B`, then Which of the following is true ?A. If matrix A is singular, then matrix B is nonsingular.B. If matrix A is nonsingular, then materix B is singular.C. If matrix A is singular, then matrix B is also singular.D. Cannot say anything.
Answer» Correct Answer - C `AB=A implies \|AB\|=\|A\|` (1) `implies \|A\|=0` or `\|B\|=1` `BA=B implies \|BA\|=\|B\|` (2) `implies \|A\|=1` or `\|B\|=0` If `\|A\|=0`, then from Eq. (2) `\|B\|=0` If `\|B\|=0`, then from Eq. (1), `\|A\|=0`

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