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If A non-singular matrix such that `(A-2l)(A-4l)=0` then A=`8A^(-1)=` . .A. IB. 0C. 3ID. 6I |
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Answer» Correct Answer - D We have `absAne0` `rArrA^(-1)` is exists Since,(A-2I)(A-4I)=0 `rArrA^(2)-A(4I)-2I(A)+8IdotI=0` `rArrA^(2)-4AI-2AI+8I=0` `rArrA^(2)-6AI+8I=0` `rArrA^(2)-6A+8I=0` On pre multiply both sides by `A^(-1)`, we get `A^(-1)A^(2)-6A^(-1)A+8A^(-1)I=0` `rArrIA-6I+8A^(-1)`=0 `rArrA-6I+8A^(-1)=0` `rArrA+8A^(-1)=6I` |
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