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(A^3)^(-1)=(A^(-1))^3 , where A is a squ...

`(A^3)^(-1)=(A^(-1))^3` , where A is a square matrix and `|A| ne 0`

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Knowledge Check

  • If A is a square matrix then A - A' is a …… matrix.

    A
    Skew symmetric
    B
    Symmetric
    C
    Diagonal
    D
    Orthogonal

  • If A is any square matrix then AA' is a ………. Matrix.

    A
    Symmetric
    B
    Skew symmetric
    C
    Identity
    D
    Diagonal

  • If [{:(3,1,-1),(0,1,2):}] then AA ' is a ……… matrix.

    A
    Symmetric
    B
    Skew symmetric
    C
    Orthogonal
    D
    None of these

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    (a.A)^(-1)=1/a.A^(-1) where a is any real number and A is square matrix

    Prove that the inverse of [[A,O],[B,C]] is [[A^(-1),O],[-C^(-1)BA^(-1),C^(-1)]] , where A, Care non-singular matrices and O is null matrix and find the inverse. [[1,0,0,0],[1,1,0,0],[1,1,1,0],[1,1,1,1]]

    Let A A=[{:(0,1),(0,0):}] , show that (aI+bA)^(n)=a^(n)I+na^(n-1)bA , where I is the identity matrix of order 2 and n in N .

    A matrix which is not a square matrix is called a ….. Matrix.

    If A is a square matrix and |A| = 2 then |A|^n = ………. . Where n is positive integer.

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