Short Quiz

If a square matrix A is such that \(\mathrm{A}^{2}=\mathrm{A}\) and \((\mathrm{I}-\mathrm{A})^{3}=\mathrm{xA}+\mathrm{I}\), then value of \(x\) must be :

If \(A=\left[a_{i j}\right]\) is an identity matrix, then which of the following is true ?

If a matrix B is such that \(\mathrm{B}\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]=\left[\begin{array}{lll}1 & 2 & 3 \\ 0 & 1 & 1 \\ 2 & 0 & 1\end{array}\right]\), then the order of matrix B is :

If A and B are square matrices of order m such that \(\mathrm{A}^2-\mathrm{B}^2=(\mathrm{A}-\mathrm{B})(\mathrm{A}+\mathrm{B})\), then which of the following is always correct?