(C) $1$. $A$ determinant is defined only for square matrices.$2$. For every square matrix $A$, there exists a unique scalar value associated with it,

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Determinant is a unique number associated with a square matrix.

(C) $1$. $A$ determinant is defined only for square matrices.$2$. For every square matrix $A$, there exists a unique scalar value associated with it, which is called its determinant, denoted by $|A|$ or $\det(A)$.$3$. Therefore, the correct statement is that a determinant is a unique number associated with a square matrix.

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

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Which of the following statements is correct regarding a determinant?

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A
Determinant is a square matrix.
B
Determinant is a number associated with a matrix.
C
Determinant is a unique number associated with a square matrix.
D
Determinant is not defined for a square matrix.

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3 and 4 .Determinants and Matrices

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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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Let $\left| {\begin{array}{*{20}{c}}{6i}&{ - 3i}&1\\4&{3i}&{ - 1}\\{20}&3&i\end{array}} \right| = x + iy$,then

EasyIIT 1998

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If $\left[\begin{array}{ccc}1 & -1 & x \\ 1 & x & 1 \\ x & -1 & 1\end{array}\right]$ has no inverse,then the real value of $x$ is

EasyAP EAMCET 2009

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In order that the matrix $\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 & \lambda & 5 \end{bmatrix}$ be non-singular,$\lambda$ should not be equal to:

Easy

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Evaluate the determinant: $\left|\begin{array}{rrr}3 & -1 & -2 \\ 0 & 0 & -1 \\ 3 & -5 & 0\end{array}\right|$

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The area of a triangle is $5$. If two of its vertices are $(2, 1)$ and $(3, -2)$ and the third vertex lies on the line $y = x + 3$,then the third vertex is

MediumIIT 1978

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Which of the following statements is correct regarding a determinant?

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Let $\left| {\begin{array}{*{20}{c}}{6i}&{ - 3i}&1\\4&{3i}&{ - 1}\\{20}&3&i\end{array}} \right| = x + iy$,then

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