Find the products AB and BA for the diagonal matrices. A=begin{bmatrix}2 & 0 0 & -3 end{bmatrix} , B=begin{bmatrix}-5 & 0 0 & 4 end{bmatrix}

Question
Matrices
asked 2021-03-04
Find the products AB and BA for the diagonal matrices.
\(A=\begin{bmatrix}2 & 0 \\0 & -3 \end{bmatrix} , B=\begin{bmatrix}-5 & 0 \\0 & 4 \end{bmatrix}\)

Answers (1)

2021-03-05
Step 1
Given matrix:
\(A=\begin{bmatrix}2 & 0 \\0 & -3 \end{bmatrix} , B=\begin{bmatrix}-5 & 0 \\0 & 4 \end{bmatrix}\)
Step 2
Now, \(AB=\begin{pmatrix}2 & 0 \\0 & -3 \end{pmatrix}\begin{pmatrix}-5 & 0 \\0 & 4 \end{pmatrix}\)
Multiply the rows of the first matrix by the columns of the second matrix :
\(=\begin{pmatrix}2\cdot(-5)+0\cdot0 & 2\cdot0+0\cdot4 \\0\cdot(-5)+(-3)\cdot0 & 0\cdot0+(-3)\cdot4 \end{pmatrix}\)
\(=\begin{pmatrix}-10 & 0 \\0 & -12 \end{pmatrix}\)
Step 3
and
\(BA=\begin{pmatrix}-5 & 0 \\0 & 4 \end{pmatrix}\begin{pmatrix}2 & 0 \\0 & -3 \end{pmatrix}\)
Multiply the rows of the first matrix by the columns of the second matrix : \(=\begin{pmatrix}(-5)2+0\cdot0 & (-5)\cdot0+0\cdot(-3) \\0\cdot2+4\cdot0 & 0\cdot0+4\cdot(-3) \end{pmatrix}\)
\(=\begin{pmatrix}-10 & 0 \\0 & -12 \end{pmatrix}\)
0

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