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Find the matrix A satisfying the matrix...

Find the matrix `A` satisfying the matrix equation `[(2, 1),( 3, 2)]A[(-3, 2),( 5,-3)]=[(1, 0 ),(0, 1)]` .

Text Solution

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Let `A=[[a,c],[b,d]]`
`[(2, 1),( 3, 2)]A[(-3, 2),( 5,-3)]=[(1, 0 ),(0, 1)]`
=>`[(2, 1),( 3, 2)][[a,c],[b,d]][(-3, 2),( 5,-3)]=[(1, 0 ),(0, 1)]`
=>`[(2a+b,2c+d),( 3a+2b, 3c+2d)][(-3, 2),( 5,-3)]=[(1, 0 ),(0, 1)]`
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Knowledge Check

  • The matrix A satisfying the equation [(1,3),(0,1)]A=[(1,1),(0,-1)] is

    A
    `[(1,4),(-1,0)]`
    B
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    C
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    D
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    A
    `[(7,5),(-11,-8)]`
    B
    `[(2,1),(5,3)]`
    C
    `[(7,1),(34,5)]`
    D
    `[(5,3),(13,8)]`

  • If [(2,1),(3,2)]A[(-3,2),(5,-3)]=[(1,0),(0,1)] then the matrix A is equal to

    A
    `[(1,1),(1,0)]`
    B
    `[(1,1),(0,1)]`
    C
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    D
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