(B) Given that $A$ and $B$ are square matrices of order $n = 3$. We know the property of determinants that $|AB| = |A| \times |B|$. So,$|AB| = (-1) \t

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(B) Given that $A$ and $B$ are square matrices of order $n = 3$. We know the property of determinants that $|AB| = |A| \times |B|$. So,$|AB| = (-1) \times (3) = -3$. We also know the property $|kA| = k^n |A|$,where $n$ is the order of the matrix. Here,$|3AB| = 3^3 |AB|$. Substituting the value of $|AB|$,we get $|3AB| = 27 \times (-3) = -81$.

Class 12 Mathematics 3-4. Matrices and Determinants Expansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line

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If $A$ and $B$ are square matrices of order $3$ such that $|A| = -1$ and $|B| = 3$,then find the value of $|3AB|$.

IIT 1988 All IIT

A
$-9$
B
$-81$
C
$-27$
D
$81$

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3-4. Matrices and Determinants

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Expansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line

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If $A$ and $B$ are square matrices of order $3$ such that $|A| = -1$ and $|B| = 3$,then find the value of $|3AB|$.

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