## Answers

(a) False

A = [a_{1} a_{2}] & B = [b_{1} b_{2}]

So, AB [a_{1}b_{1} a_{2}b_{2}]

(b) True

By the very definition of the product of 2 matrices.

(c) True

By distributive law (left) of product of matrices over addition of matrices.

(d) True

By definition & properties of the transpose of the addition of 2 matrices.

(e) False

Let us check the case for 2 matrices.

We have, (AB)^{T} = (B^{T}A^{T})

So, the transpose of a product of matrices equals the product of their transposes in the reverse order.

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