Practice question · Sort into groups
Sort each statement about inverses by whether it is true or false.
Groups: True · False
- The inverse of AB is the inverse of B times the inverse of A
- The inverse of AB is the inverse of A times the inverse of B
- When an inverse exists it is unique
- The inverse of the inverse of A is A
- Every square matrix has an inverse
Hints
- Undoing a sequence of operations requires reversing their order.
- A matrix with determinant 0 collapses space, and no matrix can undo a collapse.
Show the answer
True: The inverse of AB is the inverse of B times the inverse of A, The inverse of the inverse of A is A, When an inverse exists it is unique
False: The inverse of AB is the inverse of A times the inverse of B, Every square matrix has an inverse
Why
Products invert in reverse order — socks then shoes, shoes off then socks off — because multiplication is not commutative. Singular matrices have no inverse at all, but where an inverse exists it is unique, and inverting twice returns the original.
Practise Matrix Inverses
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More questions on Matrix Inverses
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