True or False If A and B are n times n lower triangular matrices, then AB is also lower triangular

Ayaana Buck 2020-11-30 Answered
True or False
If A and B are n×n lower triangular matrices, then AB is also lower triangular
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Expert Answer

Khribechy
Answered 2020-12-01 Author has 100 answers

Step 1
Given,
A and B are nxn lower triangular matrices.
Consider 2×2 lower triangular matrix
A=[a0bc] and B=[d0ef]
Now taking multiplication of A and B we get,
AB=[a0bc][d0ef]
AB=[ad0bd+cecf]
Step 2
Therefore,
AB is also an upper triangular matrix,
Hence,
If A and B are n×n lower triangular matrices, then AB is also lower triangular
Therefore,
Given statement is true.

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Jeffrey Jordon
Answered 2022-01-22 Author has 2064 answers

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