Is the product of two invertible matrices also invertible?

Answer 1

Yes

Matrix multiplication is associative, so #(AB)C = A(BC)# and we can just write #ABC# unambiguously.
Suppose #A# and #B# are invertible, with inverses #A^-1# and #B^-1#. Then #B^-1A^-1# is the inverse of #AB#:
#(AB)(B^-1A^-1) = ABB^-1A^-1 = AIA^-1 = A A^-1 = I#
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Answer 2

Yes, the product of two invertible matrices is also invertible.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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