Consider a block matrix , where role="math" localid="1660371822794" are square matrices. For which choices of is A invertible? In these cases, what is ?
The matrix A is invertible when are invertible.
The invertible matrix is, .
Consider where role="math" localid="1660372094980" are square matrices. We want to find what choices of make A invertible and what is for these choices.
Obviously, A will be invertible only if are invertible.This is because if are invertible they can reduce to the identity which means that A can reduce to the identity as well.
Logically this means that, .
Now, check it by finding the product of .
Where the product is identity matrix.
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