An- n and Bn- n are diagonal matrices then AB -matrix

The correct options are A diagonal D squareWe know A_m× nB_n× p=(AB)_m× p Thus A_n× nB_n× n=(AB)_n× n , which is clearly a square matrixAlso since bot ...

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Standard XII

Mathematics

Multiplication of Matrices

An× n and B...

Question

$A_{n \times n}$ and $B_{n \times n}$ are diagonal matrices then AB $=$ ..............matrix

square

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diagonal

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scalar

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rectangular

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Solution

The correct options are
A diagonal
D square
We know $A_{m \times n} B_{n \times p} = (A B)_{m \times p}$
Thus $A_{n \times n} B_{n \times n} = (A B)_{n \times n}$ , which is clearly a square matrix
Also since both $A$ and $B$ are diagonal matrix, so their product will also be a diagonal matrix.
Hence, both options A and B are true.

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An×n and Bn×n are diagonal matrices then AB=..............matrix

The correct options are A diagonal D squareWe know Am×nBn×p=(AB)m×pThus An×nBn×n=(AB)n×n, which is clearly a square matrixAlso since both A and B are diagonal matrix, so their product will also be a diagonal matrix.Hence, both options A and B are true.

$A_{n \times n}$ and $B_{n \times n}$ are diagonal matrices then AB $=$ ..............matrix