st","extracted_subject":"MATH","extracted_chapter":"DETERMINANTS AND MATRICES","extracted_topic":"SPECIAL TYPES OF MATRICES, TRANSPOSE, ADJOINT AND INVERSE OF MATRICES","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_2208.png?top_left_x=532&top_left_y=1066&width=532&height=403&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e74425d76b7ab320fba","slug":"if-a-beginbmatrix-i---i---i-i-endbmatrix-b-beginbm","content":"If A= \\(\\begin{bmatrix}\ni & - i \\\\\n - i & i\n\\end{bmatrix}\\), B = \\(\\begin{bmatrix}\n1 & - 1 \\\\\n - 1 & 1\n\\end{bmatrix}\\), then A⁸ equals","options":[{"_id":"68a386987f15af4716b7d45d","text":"4B","sequence":0,"isCorrect":false},{"_id":"68a386987f15af4716b7d45e","text":"128B","sequence":1,"isCorrect":true},{"_id":"68a386987f15af4716b7d45f","text":"–128B","sequence":2,"isCorrect":false},{"_id":"68a386987f15af4716b7d460","text":"– 64B","sequence":3,"isCorrect":false}],"correct_answer":"128B","explanation":"we have A = iB\n\nŽ A² = (iB)² = i²B² = –B²\n\n= \\(\\begin{bmatrix}\n2 & - 2 \\\\\n - 2 & 2\n\\end{bmatrix}\\) = – 2B\n\nŽ A⁴ = (–2B)² = 4B² = 4(2B) = 8B\n\nŽ A⁸ = (A⁴)² = (8B)² = 64B² = 128B","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:40.394Z","__v":0,"vector_store_id":"4147d565-f421-405b-8a04-0aedbca52000","updated_at":"2024-08-30T21:49:40.394Z","isStarred":false},"params":{"questionSlug":"if-a-beginbmatrix-i---i---i-i-endbmatrix-b-beginbm"}}]}]]

Question: If A= \(\begin{bmatrix} i & - i \\ - i & i \end{bmatrix}\), B = \(\begin{bmatrix} 1 & - 1 \\ - 1 &...

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