Let a determinant is given - JEE Main Maths Physics

Determinant Operations and Value Relations

Structure of the Given Determinant A determinant $A$ is defined with elements arranged as $a, b, c$ in the first row, $p, q, r$ in the second row, and $x, y, z$ in the third row. The value of $\det(A)$ is given as...

If x, y, z are in arithmetic progression with common
difference d, x ≠ 3d, and the determinant of the matrix $342x452y5kz$ is zero, then the value of k² is:

72

If [ ] denotes the greatest integer less than or equal to the real number under consideration and

–l ≤ x < 0, 0 ≤ y < 1, 1 ≤ z < 2, the value of the determinant $\left[x\right]+1\left[y\right]\left[z\right]\left[x\right]\left[y\right]+1\left[z\right]\left[x\right]\left[y\right]\left[z\right]+1$ is

[<em>z</em>]

The value of the determinant $bcacababc{a}^3{b}^3{c}^3$ is

(<em>a</em>² &ndash; <em>b</em>²)(<em>b</em>² &ndash; <em>c</em>²)(<em>c</em>² &ndash; <em>a</em>²)

If A is an invertible matrix of order 2, then det (A^&ndash;1) is equal to

<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><mi>det</mi><mfenced><mi>A</mi></mfenced></mrow></mfrac></math>