Question

The commutative property holds for the __of two matricies but does not hold __ for the of two matricies.

Answer 1

Addition and multiplication

Explanation:

The commutative property holds good for the addition of two matrices.

Because addition of matrices mean adding the corresponding entries. Since addition is commutative we have addition of matrices which involve adding the corresponding entries is also commutative

But product of two matrices is not commutative.

Eg: Consider A =
`\left[\begin{array}{ccc}1&0&0\\4&1&1\\7&2&3\end{array}\right]`

and B =
`\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right]`

We get AB =
`\left[\begin{array}{ccc}1&2&3\\15&21&27\\36&48&60\end{array}\right]`

and BA =

`\left[\begin{array}{ccc}30&8&11\\66&17&23\\102&26&35\end{array}\right]`

proving AB not equals BA.

Answer 2

The commutative property holds for the Addition of two matricies but does not hold subtraction for the of two matricies.