Invertible matrices and determinants | Matrices | Precalculus | Khan Academy
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Invertible matrices and determinants | Matrices | Precalculus | Khan Academy
An invertible matrix is a matrix that has an inverse. In this video, we investigate the relationship between a matrix's determinant, and whether that matrix is invertible.
34.8K viewsApr 7, 2021
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Invertible Matrix Examples
4. (9 points) Give examples of A and B such that(a) A B is not invertible although A and B are invertible.(b) A B is invertible although A and B are not invertible(c) All of A, B and A B are invertible.(d) In the last case, show that B^-1 A^-1 is also invertible and find a formula for its inverse.(Hint: Check this out A^-1(A B)B^-1)
4. (9 points) Give examples of A and B such that(a) A B is not invertible although A and B are invertible.(b) A B is invertible although A and B are not invertible(c) All of A, B and A B are invertible.(d) In the last case, show that B^-1 A^-1 is also invertible and find a formula for its inverse.(Hint: Check this out A^-1(A B)B^-1)
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