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CUET UG 2022 Applied Mathematics

Let A and B be two non-zero square matrices and AB and BA both are defined. It means

Solution

Let A be of order $m \times m$ and B be of order $n \times n$.

For AB to be defined: number of columns of A = number of rows of B
⇒ $m = n$

For BA to be defined: number of columns of B = number of rows of A
⇒ $n = m$

Hence $m = n$, so both matrices must have same order.
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