True or FalseIf A and B are nxxn lower triangular matrices, then AB is also lower triangular

opatovaL 2021-03-05 Answered

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

 

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falhiblesw
Answered 2021-03-06 Author has 97 answers

Consider 2 x 2 lower triangular matrix

A=[a0bc]andB=[d0ef]

Now taking multiplication of A and B we get,

AB=[a0bc][d0ef]

AB=[ad0bd+cecf]

Therefore, AB is also an upper triangular matrix, N

Hence, if A and B are n x n lower triangular matrices, then AB is also lower triangular. Therefore, given statement is true.

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