First slide

Transpose of matrix

Question

If A, B, and C arc three square matrices of the same order, then $AB = AC \Rightarrow B = C$ . Then

Moderate

A

$| A | \neq 0$
B

A is invertible
C

A may be orthogonal
D

A is symmetric

Solution

If $| A | \neq 0$ , then
AB = AC
or $A^{- 1} AB = A^{- 1} AC$
or B = C
Also, if A is orthogonal matrix, then, AA^T = I
$\Rightarrow |{AA}^{T}| = 1 \Rightarrow | A |^{2} = 1 \Rightarrow A$ is invertible

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