Maths. Section B1Determinants

Let A = [a_ij]_2×3 and B = [b_ij]_3×2, then |5AB| is equal to

Let $A = [a_{ij}]_{2×3}$ and $B = [b_{ij}]_{3×2}$, then $|5AB|$ is equal to

Answer & explanation

Correct answer: option 3

The correct answer is Option (3) → $5^2|AB|$

$A$ is of order $2\times3$ and $B$ is of order $3\times2$

Hence $AB$ is a square matrix of order $2\times2$

Property of determinant

$|kM|=k^n|M|$ for an $n\times n$ matrix $M$

Here $AB$ is $2\times2$ and scalar multiplier is $5$

$|5AB|=5^2|AB|$

The value of $|5AB|$ is $5^2|AB|$.