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If |–a b c; a –b c; a b –c| = kabc, then the value of k is :
If |A| = |kA|, where A is a square matrix of order 2, then sum of all possible values of k is
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The value of |x+y, y+z, z+x; z, x, y; 1, 1, 1| is
If A and B are two square matrices of order 2 and |A| = 2 and |B| = 5, then |– 3AB | is :
Obtain the value of Δ = |[1+x, 1, 1], [1, 1+y, 1], [1, 1, 1+z]| in terms of x, y and z. Further, if Δ = 0 and x, y, z are non-zero real numbers, prove that x⁻¹ + y⁻¹ + z⁻¹ = −1.
If Δ₁ = |1 0 0; 0 2 0; 0 0 3| and Δ₂ = |0 2 0; 1 0 0; 0 0 6|, then
