Matrices · Mathematics · Class 12

If for a square matrix $$\mathrm{A}, A^2-A+I=\mathrm{O}$$, then $$\mathrm{A}^{-1}$$ equals:

$$\text { If } A=\left[\begin{array}{ll} 1 & 0 \\ 2 & 1 \end{array}\right], B=\left[\begin{array}{ll} x & 0 \\ 1 & 1 \end{array}\right] \text { and } A=B^2 \text {, then } x \text { equals: }$$

$$\text { If } A=\left[\begin{array}{ccc} 1 & 2 & 3 \\ 3 & -2 & 1 \\ 4 & 2 & 1 \end{array}\right] \text {, then show that } A^3-23 A-40 I=O \text {. }$$