st","extracted_subject":"MATH","extracted_chapter":"DETERMINANTS AND MATRICES","extracted_topic":"TYPES OF MATRICES, ALGEBRA OF MATRICES","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_2191.png?top_left_x=532&top_left_y=1155&width=532&height=212&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e74425d76b7ab320e2e","slug":"the-inverse-of-a-skew-symmetric-matrix-if-it-exist","content":"The inverse of a skew symmetric matrix (if it exists) is –","options":[{"_id":"68a3a34e7f15af4716bcc53b","text":"A symmetric matrix","sequence":0,"isCorrect":false},{"_id":"68a3a34e7f15af4716bcc53c","text":"A skew symmetric matrix","sequence":1,"isCorrect":true},{"_id":"68a3a34e7f15af4716bcc53d","text":"Diagonal matrix","sequence":2,"isCorrect":false},{"_id":"68a3a34e7f15af4716bcc53e","text":"None of these","sequence":3,"isCorrect":false}],"correct_answer":"A skew symmetric matrix","explanation":"We have A¢ = – A\n\nNow, AA^–1 = A^–1 A = I_n\n\nŽ (AA^–1)¢ = (A^–1 A)¢ = (I_n)¢\n\nŽ (A^–1)¢ A¢ = A¢(A^–1)¢ = I_n\n\nŽ (A^–1)¢ (–A) = (–A) (A^–1)¢ = I_n Thus, (A^–1)¢ = –(A^–1)\n\n[inverse of a matrix is unique].","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:40.298Z","__v":0,"vector_store_id":"35d7b174-142d-4bac-b8dd-f1442db1b7fa","updated_at":"2024-08-30T21:49:40.298Z","isStarred":false},"params":{"questionSlug":"the-inverse-of-a-skew-symmetric-matrix-if-it-exist"}}]}]]

Question: The inverse of a skew symmetric matrix (if it exists) is –...

Solution