\ begin {ecuación*}\ begin {alineado}\ left [\ begin {array} {r|r} A & I\ end {array}\ right] & {} = {}\ left [\ begin {array} {r|rrrr} A &\ mathbf e_1 &\ mathbf e_2 &\ ldots\ mathbf e_n\ end {array}\...\ begin {ecuación*}\ begin {alineado}\ left [\ begin {array} {r|r} A & I\ end {array}\ right] & {} = {}\ left [\ begin {array} {r|rrrr} A &\ mathbf e_1 &\ mathbf e_2 &\ ldots\ mathbf e_n\ end {array}\ derecha]\ & {} sim\ {}\ left [\ begin {array} {r|rrrr} I &\ mathbf b_1 &\ mathbf b_2 &\ ldots\ mathbf b_n\ end {array}\ right] =\ left [\ begin {array} {r|r} I & A^ {-1}\ end {array}\ right]\ text {.} \ end {alineado}\ end {ecuación*}
