Let M be a 3 × 3 invertible matrix with real entries and let I denote the 3 × 3 identity…
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
Let M be a 3 × 3 invertible matrix with real entries and let I denote the 3 × 3 identity matrix. If M−1 = adj(adj M), then which of the following statements is/are ALWAYS TRUE?
- M = I
- det M = 1
- M2 = I
- (adj M)2 = I
Answer
(D) (adj M ) 2 = I
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- If f(θ) = | array ccc 1 & 1 & -1 1 & e^ i & 1 1 & -1 & -e^ -i array | then
- Let | M | denote the determinant of a square matrix M . Let g: [0, 2 ] R be the function defined by g( heta)=…
- Let M= [ array lll 0 & 1 & a 1 & 2 & 3 3 & b & 1 array ] and adj M= [ array ccc -1 & 1 & -1 8 & -6 & 2 -5 & 3…
- If ∆ = | array lll 1 & a & ~b 1 & ~b & a 1 & c & ~b array | = | array lll 1 & a & a ^ 2 1 & ~b & ~b ^ 2 1 & c…
- If A = [ array cc 1 & x - x & 1 array ] , then the value of |A T A –1 | is
- Which of the following values of α satisfy the equation | array ccc (1+ )^ 2 & (1+2 )^ 2 & (1+3 )^ 2 (2+ )^ 2…
- Suppose D = | array lll a _ 1 & ~b _ 1 & c _ 1 a _ 2 & ~b _ 2 & c _ 2 a _ 3 & ~b _ 3 & c _ 3 array | and D’ =…
- Let M and N be two 3 × 3 matrices such that MN = NM . Further, if M ≠ N 2 and M 2 = N 4 , then
More Matrices and Determinants questions · Browse all practice questions