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Matrices

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Question : 21 of 36

Marks: +1, -0

Let

A^{\top}

be the transpose of matrix

A

m \times n

A^{\top} A

is a matrix of order

$n \times n$
$m \times m$
$m \times n$
$n \times m$

Solution:

Concept:

When multiplying two matrices, the order of the product is determined by the outer dimensions of the factors.

Explanation:

Given matrix

A

has order

m \times n

(rows × columns).

Its transpose

A^\top

has order

n \times m

.

Multiplying

A^\top

(order

n \times m

) by

A

(order

m \times n

) gives a product of order

n \times n

.

Answer:

n \times n

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