Maths-
General
Easy
Question
If A =
, then for every positive integer n, An is equal to -
- None of these
The correct answer is: ![open square brackets table row cell 1 plus 2 n end cell cell negative 4 n end cell row n cell 1 minus 2 n end cell end table close square brackets](data:image/png;base64,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)
we are given A and need to find ![A to the power of n](data:image/png;base64,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)
![A equals open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets
therefore A squared equals open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets
space equals open square brackets table row 5 8 row 2 5 end table close square brackets
therefore A cubed equals open square brackets table row 5 8 row 2 5 end table close square brackets open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets space
therefore A cubed space equals open square brackets table row 7 12 row 3 7 end table close square brackets
therefore A to the power of 4 equals open square brackets table row 7 12 row 3 7 end table close square brackets open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets
therefore A to the power of 4 space equals open square brackets table row 9 16 row 4 9 end table close square brackets
therefore A to the power of n space space equals open square brackets table row cell 1 plus 2 n end cell cell 4 n end cell row cell space n end cell cell space space space space space space space space 1 plus 2 n space space end cell end table close square brackets](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOwAAAGWCAYAAAB7HW8HAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAADKu5W5MAAAFoxJREFUeNrtnX+EXUm+wMtoMUYbRjyjRYRo0WJEWGu1iGjWWK09LYxoMSKaMSJGrDB/rfzxhHj2jxj5J2KtJ1aIMSJahIiIiBWiRTwRTRtrPev9M39EjKsNd+u7Vb25c+fcc8499ePUOfX58CW5t/ueqlP16VN1Tt1vKdUew4LoE32vH2TGkPoC0IGpL0DLHXhJxz0dP+oY6NjScVXH3hbKvdJQPoSFbIR9pOOkjj0jrx3VcT9ymWd1vEJYQNhmvIlc5us61hEWEHZ6Dup4HbG8x3Q8dCg7wkKWwn6s46ydxy5HKqsMxV/qOICwgLD1f340LkQs6xUd5x3lQ1jI8gr7kY5VHc90nGh43KoY5YiOpx7KjrCQ9Rx21kobGjnGPMICwroziFTOuldjhAWEnYAMVbc6VHaEhWyEfazjMx0zOt5TZuXT9zrOICzAOy4k0umP69iwQ2AJWfm00rHRAcJCUE7p2LFXtVTnsLnN2QEKkUcnslDggTKPUOjA1BcSRtbMrtk54jU6MPWFdFm080VBlgFu1+iITR59ICyAIzJffa5j/8hrmzoW6MDUF9Ljko6LY69d1nGODkx9IS0W7NV0HFmve5chMcJCWjwpES7E4x2EBWjIF8rkSJrELeX/u6cIC9CAOWWeuc6W/Mx6hdB0YOoLkbitqpf57VP+F9ojLAAdmPoCpNKBD+n4g44XLZTX9dgIC9kJe1OZG2RtdH7XYyMsZDtEHHaw3AgLCIuwAAiLsAAIC4CwTX7XJRMiwgLCcoUFQFiEBUBYhAWERViAngnrslWGj/K6HBthIdsrLPUFoANTX4AUh7fUDwAAAAAAAAAAAAAAAAAAAAAAAAAakPPyR5Z+QicbNdf68uUKoBERlraGNBpxScc9HT/qGCizW59ssbm3hXKvqOZf8KfukIWwj3Sc1LFn5LWjOu5HLrPs0/sqsrB9qztkPEx6E7nM15XZQDumsH2rO2Qq7EEdryOW95iOhw5lH1J3yFHYj3WctXO55UhlleHoSx0HWha2D3WHTIQdf653IWJZr+g479gBh9QdcrzCfqRjVcczHScaHnea/XuO6HjqoexD6g4hZZLYsQ02n+AcdtZ23NA8K6h/23PYLtcdAvKejnM6NhMUVhhE/OPVZDe9UMJ2ue4QgUGCwspwbatDw/khdYcYyFzpccsNL8f/TMeMverL6p/vdZzJQNi+1R0cqLrbOGfnsAdbbvjjOjbslV5CVv+stDzHjyVs3+oODTmlzE2lmQnvH7IdZS6hhu8yLP6HxsjjAXkY/kCZxwRFV1ZZcP4hjYiwtLXfE9HkZMi60DU7D7pW8L7IukAjIixt3b6wi3aoK8hSt+2Sz61zC3/ah/F0WoSFmsh89bmO/SOvbUa4mtKICAsNuKTj4thrl5VZHEEjIixtnRALqnjFkjxnvethWM6QGGER1iNPSoQqe7xDIyIsbe14NSti1b53q+C9L5TJAzQJ+Z1lGhFhaev2hZVnqvLMdbbkc9crhKYREZa2jsRtVb2UbZ+Kv5gcYREWaESEpa0hlUaU9c1/0PGihfK6HntI3SE3YW8qcwOtjQ7geuwhdYdch0nDDpZ7SN0BYREWYQFhERZhAWGpOyBsg991yQbYZWFTqDsgLFdYrrCAsAiLsECnRVhAWIRFWEiu8V22i/BRXpdjD6k75HqF7Xp9WfwPNCLC0taQ7jCry/XLue4AAAAAAAAAAAAAAAAAAAAAAADQS7q0dIxlboCwlB2ATk/ZAVru9E0z7BXxgY5vdLzVMdBxX5md8xAWwKOwvviTjsvK7Pa+R8cVHc8QFiBNYQdj/39Pxw7CAqQprAyFZ8eE/TvCAqQprMxfvxr5/6KOPyIsgF9hZdj6Rsc9Hb8fu0pOwxH7WRKPdfxDx3GEBfDf6eVG0a+U2Yn7tY6FKX//gI6/6JhT5oaTsp+3bUVGWIBAnf5Te4Wchu8miLmk4xHCAoTt9AOPPz9AWIBwnf4TO5Sdhlc65gteP2znsggL4KHTy1BW7ua+Z+N3VtaTUx7zpJV2aeSzluxnfYmwAH46/Wc6tnT8pOMHHbd1/LrhceWzNpW5Szyw8+DVFobzANnNYSk7AJ0eYQEQFiCRzlsVCAvAFZayA9DpERYYEiMsAFdYyg5Ap0dYAIQFoNNTdgA6PcICNOz0x3R8q0yKGFm0/0LH6YbH9JHfGGEBYUuQb9SsqXd5nOT7q0/ta22IhrCAsFMi+ZleIixAd+aBA4QF6Iawi3ZYjLAAiQv7vjL74RxrcEwf+Y0RFhC2Jh/puKNMmtOmuOY3RlhA2BoctLLOeyxHk/zGCAsIW4FcBW8os7+rbwYIC+Cv03+sTKbEmQDlaJLfGGEBYUvYaDDPLMJXfmOEBYSt+FkfSwp95TdGWEBYyg5Ap6fsAJ46vcvwlrICAAAAAAAAAAAAAAAAAAAAAAAAQGL0ZXlk35dOsjQU/t0R+lD2Ie0GNDzC0m7Q2Yb39SV6QfJSfaPjrTL5pO7r2BdJ2CVlUrz+aI8tX+i/qmNvC+d/peH5Q1iEjdpJ/qTjsjI5qvbouKJMnuUYwj5SJiXOnpHXjto/GjGRfNCvEBa6IOx4lkbJL7XT8pD4TeRzf13HOsJCF4R9q36+44AI+/cWhZV8z68jnnfZseGhQ9kRFmGjdhKZv3418n/J5PjHFoSV9LFn7Tx2OdI5l6G47Dp4AGEhtLA+9uURjtjPkpBdB/6h43hEYcdvml2IeM5lvn7eUT6ERdjauO7LI1eWv+iYU+9u/MjnbVuRY15hZZ+iVWVueJ1oeP6qYvwP1VMPbYCwicq0e1V7odw2vwrV8E325flugpjyuOVRS3PYWTX9XeomyDHmEbb/yFXsbwkKKww8/vygJWGb1MPlj7Dr82yETRy5i/pDgsI22ZfnlSrefe+wncu2Iaxc8bc6NC1B2ISRFTjXlLmb2WZn8bUvz0kr7dLIZy3Zz/oygrAyhP/MzsV3j/29jjMIC3W4UGMI9XkCncXXvjy7n7Vp5+cDK9GqQ9mnqYfcjd6wxx3YefNKy/cqELYjnLKdtmwbyQ+VWcb3RaJz2BQ6Oov/ITjySEEeoD+oeXUZ0PAIi7B+Tl6TEyhrSdfs3OlajWHccxoeYRG2HWEX7TxKkOVx2yWfu/v1swM1yjDtIwOERVioYMZeLfePvCY3YBZoeIRF2PS4pOPi2GtyU+kcDY+wCJsWC/ZqOo6sY73rYVjOkBhhwSNPSoSqerxDwyMswjpczYpYte/dKnhPnqNeLflc+Z1lGh5hEbZ9YeWrZPLMtez7o+sVQtPwCIuwkZBlfFXL3yRr4BYNj7AICwhLu0FmDS+Jw75VJkXM7pfqTztMKVzzG7sKe0iZrBkvWjjvrsdGWIStRL5RszYyD5fvrz61r7XR2VyFvanMjcA2Or/rsREWYRshyyVfdlTYFDo/wkL0hh8gLMJCN4RdVL/MAoiwCAsJCvu+MlkAjzU4po/8xggLCFsT+fL9HeWWetU1v3EKwjZdw42wEK3hD1pZ5z2Wo0l+Y66wgLAVyFXwhjL7u/pmgLAIC/4aXjJj3FZhvlHUJL8xwgLClrCh/GTF8JXfGGEBYSt+1seSQl/5jV2Fda2H63n3tSwTELZzZWfxP9DwCEu7QXoN39aw0GdZu1SPvrcTAAAAAAAAAAAAAAAAAAAAAAAAwAh9XALHsj7otbDUEYDOTB0B2uzMLtkCi6jab8bn3j4AXH0sklHiRoPfq9pvJrW9fQA6L6wkanuiTJLxGGVoc28fgM4Le1fH0chlGCAsIOz0fGnnoDHL0ObePgCdFVaGprLPzkzEMrjs7QOQtbByQ2gpYhlc9vZBWAgmz+5Oby+U28ZTITuz3BW+F7EMrnv7ICwERzLu/y1BYSVzv+w8dzRSGXzs7YOwEBwR44cEhV1V0+8617QMvvb2QVgIyl4d13ScTVDYWwHKNakMvvb2QVhw4kKNeeznEefN0/D/ytwA8jlnn7S80dcySISFxpxS5qZS2TDvQx2XlVm2l5qwXQRhoRFyZZJldQ/sXLCKAZ2ZOoK/ody0XFdm4foZO0ct47iO53Rm6gjtCCtL6jbsv+Xu53bJ58qV9b4yq4lc5oN15n0ICzDGjL1a7h95bVP5uQNKZ6aO4JlLOi6OvSY3lc7RmakjpMWCvZqOc0KZr6b5HqYzJEZYcOBJiUBVj3fozNQRHK5eRaza924VvCfPUa+WfK78zjKdmTpC+8LOKfPMdbbkc9crhKYzU0eIhCxaX6n4mX06tujM1BGAzoywkHlnlgwT8sX1H5VZ3LFlh/R7PU47fOU8RljIXthHOk7q2DPymnyR/X7A8jXNeYywwHBxAm8Clc1HzmOEBYQdQfItvQ5UNh85jxEWENZe/c7aeWyIZ8m+ch4jLGQt7PjNoAsByuQz5zHCAldYZb6Mv2rFOuG5TD5zHiMsIOwIs1ZaX/jOeYywgLBj+EplEyLnMcICwo5wRPlbXhki5zHCQrbCPrZD1hl7NZR55vfK5KjyQYicxwgL2QorieE27BBYQlY+rXgsi8+cxwgLDImpIwCdmToCTNGZfX4zhjoBAAAAAAAAAAAAAAAAAAAAAAAAZEVuSxH7vkyRZZgZCJtTHYe0L9CgCEv7QnIN6nu/m0PK5Bp+MeH9Yzq+VWYngR37c6cjChty76BpWWl4jhGWv8C/oOl+NzeV2eR6UhkkBc2aeren7mEdT+1rMYRtY++gIqT+rxAWfDSoj/1upimDJBV/2fKQ+E3kNrquzGbfCAvODepjv5tpyzBoUdiQewdNmhY8dCg7wiLsv/G13800ZVi0w+LYwobeO6iIPXY0cQBhwbVBfe53U7cM79tjHosobIy9gyZxRcd5x7ZCWIT9Fz73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)
Therefore the correct option is choice 2
Related Questions to study
Maths-
If A = [aij] is scalar matrix of order n × n such that aij = k for all i, then |A| equals -
If A = [aij] is scalar matrix of order n × n such that aij = k for all i, then |A| equals -
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